Show or hide registration fields based on selected

I am trying to customize the registration form for my site. I've been using this guide and have successfully created/stored additional fields for my registration form. Guide to customized Registration.

I have created a drop-down/select field in my registration form for the user to select whether they want a Standard or Education account-type when registering:

If they select the Education account type, I want additional fields to appear so that I can collect additional data for their school. Is there a way for me to provide conditional logic for whether or not a field is visible based on the current value of another field in the form?

Here's kind of an example of what I would want to accomplish:

Can someone point me in the right direction to accomplish conditional form fields? Also, I do not want to use a third-party plugin for this. Having full control is important for this.

EDIT: As requested, here is the full code for my function:

    <?php
/*
Plugin Name: Custom Account Fields
Plugin Author: Case Silva
*/

//Create Custom Fields
if(!function_exists('get_custom_fields')){
    function get_custom_fields(){
        return apply_filters('custom_fields', array(
            'verified_education_acct' => array(
                'type' => 'checkbox',
                'label' => __('Verified?'),
                'required' => false,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_registration' => true,
                'hide_in_checkout' => true
            ),
            'customer_id_num' => array(
                'type' => 'text',
                'label' => __('Customer ID# '),
                'placeholder' => __('e.g. 1234567890'),
                'required' => false,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_checkout' => true,
                'hide_in_registration' => true
            ),
            'account_type' => array(
                'type' => 'select',
                'label' => __('What type of account will this be?'),
                'options' => array(
                    '' => __('Select an option...'),
                    1 => __('Education'),
                    2 => __('Standard')
                ),
                'required' => true,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_checkout' => false,
                'hide_in_registration' => false
            ),
            'school_name' => array(
                'type' => 'text',
                'label' => __('School Name'),
                'placeholder' => __('e.g. North Middle School'),
                'required' => true,
                'hide_in_account' => 'account_type' != 1,
                'hide_in_admin' => false,
                'hide_in_checkout' => 'account_type' != 1,
                'hide_in_registration' => 'account_type' != 1
            ),
        ));
    }
}

//Add them to User Area
if(!function_exists('print_user_frontend_fields')){
    function print_user_frontend_fields(){
        $fields = get_custom_fields();
        $user_logged_in = is_user_logged_in();

        foreach ($fields as $key => $field_args) {
            if($user_logged_in && !empty($field_args['hide_in_account'])){
                continue;
            }
            if(! $user_logged_in && ! empty($field_args['hide_in_registration'])){
                continue;
            }
            woocommerce_form_field($key, $field_args);
        }
    }
}

//Add them to Admin Area
if(!function_exists('print_user_admin_fields')){
    function print_user_admin_fields(){
        $fields = get_custom_fields();

        ?>
        <h2><?php _e('Education/School Information'); ?></h2>
        <table class = "form-table" id = "additional-information">
            <tbody>
                <?php foreach ($fields as $key => $field_args) { ?>
                    <?php
                    if(! empty($field_args['hide_in_admin'])){
                        continue;
                    }

                    $user_id = get_edit_user_id();
                    $value = st_get_userdata($user_id, $key);
                    ?>
                    <tr>
                        <th>
                            <label for="<?php echo $key; ?>"><?php echo $field_args['label']; ?></label>
                        </th>
                        <td>
                            <?php $field_args['label'] = false; ?>
                            <?php woocommerce_form_field($key, $field_args, $value); ?>
                        </td>
                    </tr>
                <?php } ?>
            </tbody>
        </table>
        <?php
    }
}

//Save them to the database
if(!function_exists('save_acct_fields')){
    function save_acct_fields($customer_id){
        $fields = get_custom_fields();
        $sanitized_data = array();

        foreach ($fields as $key => $field_args) {
            if(! is_field_visible($field_args)){
                continue;
            }

            $sanitize = isset($field_args['sanitize']) ? $field_args['sanitize'] : 'wc_clean';
            $value = isset($_POST[$key]) ? call_user_func($sanitize, $_POST[$key]) : '';

            if(is_userdata($key)){
                $sanitized_data[$key] = $value;
                continue;
            }

            update_user_meta($customer_id, $key, $value);
        }

        if(! empty($sanitized_data)){
            $sanitized_data['ID'] = $customer_id;
            wp_update_user($sanitized_data);
        }
    }
}

//Check if field is visible on page
if(!function_exists('is_field_visible')){
    function is_field_visible($field_args){
        $visible = true;
        $action = filter_input(INPUT_POST, action);

        if(is_admin() && ! empty($field_args['hide_in_admin'])){
            $visible = false;
        } elseif((is_account_page() || $action === 'save_account_details') && is_user_logged_in() && ! empty($field_args['hide_in_account'])){
            $visible = false;
        } elseif((is_account_page() || $action === 'save_account_details') && ! is_user_logged_in() && ! empty($field_args['hide_in_registration'])){
            $visible = false;
        } elseif(is_checkout() && ! empty($field_args['hide_in_checkout'])){
            $visible = false;
        }
        return $visible;
    }
}

//Check if field is predefined
if(!function_exists('is_userdata')){
    function is_userdata($key){
        $userdata = array(
            'user_pass',
            'user_login',
            'user_nicename',
            'user_url',
            'user_email',
            'display_name',
            'nickname',
            'first_name',
            'last_name',
            'description',
            'rich_editing',
            'user_registered',
            'role',
            'jabber',
            'aim',
            'yim',
            'show_admin_bar_front'
        );
        return in_array($key, $userdata);
    }
}

//Populate form with submitted data
if(!function_exists('get_edit_user_id')){
    function get_edit_user_id(){
        return isset($_GET['user_id']) ? (int) $_GET['user_id'] : get_current_user_id();
    }
}

//Access saved data
if(!function_exists('st_get_userdata')){
    function st_get_userdata($user_id, $key){
        if(!is_userdata($key)){
            return get_user_meta($user_id, $key, true);         
        }

        $userdata = get_userdata($user_id);

        if(!$userdata || ! isset($userdata->{$key})){
            return '';
        }

        return $userdata->{$key};
    }
}

add_action('woocommerce_register_form', 'print_user_frontend_fields', 10);
add_action('woocommerce_edit_account_form', 'print_user_frontend_fields', 10);

add_action('show_user_profile', 'print_user_admin_fields', 30);
add_action('edit_user_profile', 'print_user_admin_fields', 30);

add_action('woocommerce_created_customer', 'save_acct_fields');
add_action('personal_options_update', 'save_acct_fields');
add_action('edit_user_profile_update', 'save_acct_fields');
add_action('woocommerce_save_account_details', 'save_acct_fields');
?>

The only way to show hide fields is to use Javascript/jQuery as it's a event on client side.

So I have made some small changes to your code adding the necessary jQuery to handle Showing and hiding school_name text field depending on the account_type select field live event choice.

Here are the Two functions that I have changed in your code:

// Get custom fields
if(!function_exists('get_custom_fields')){
    function get_custom_fields(){
        return apply_filters('custom_fields', array(
            'verified_education_acct' => array(
                'type' => 'checkbox',
                'label' => __('Verified?'),
                'required' => false,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_registration' => true,
                'hide_in_checkout' => true
            ),
            'customer_id_num' => array(
                'type' => 'text',
                'label' => __('Customer ID# (Acumatica)'),
                'placeholder' => __('e.g. 1234567890'),
                'required' => false,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_checkout' => true,
                'hide_in_registration' => true
            ),
            'account_type' => array(
                'type' => 'select',
                'label' => __('What type of account will this be?'),
                'class' => array('form-row-wide'),
                'options' => array(
                    '' => __('Select an option...'),
                    1 => __('Education'),
                    2 => __('Standard')
                ),
                'required' => true,
                'hide_in_account' => true,
                'hide_in_admin' => false,
                'hide_in_checkout' => false,
                'hide_in_registration' => false,
                'js_trigger' => true, // <===  <=== Enabling Javascript 
            ),
            'school_name' => array(
                'type' => 'text',
                'label' => __('School Name'),
                'class' => array('form-row-wide off'), // <===  <===  Hidden field
                'placeholder' => __('e.g. North Middle School'),
                'required' => true,
                'hide_in_account' => false,
                'hide_in_admin' => false,
                'hide_in_checkout' => false,
                'hide_in_registration' => false,
                'js_triggered_by' => 'account_type', // <===  JS: field that trigger show/hide
                'js_show_val' => '1', // <===  <=== JS: selected field value that show this field 
            ),
        ));
    }
}

//Add them to User Area
if(!function_exists('print_user_frontend_fields')){
    function print_user_frontend_fields(){
        $fields = get_custom_fields();
        $user_logged_in = is_user_logged_in();
        $enable_js = false; // Initializing
        $data_js = []; // Initializing

        // Hiding conditional field (with "off" class)
        echo '<style>p.form-row.off{display:none;}</style>';

        foreach ($fields as $key => $field_args) {
            if($user_logged_in && !empty($field_args['hide_in_account'])){
                continue;
            }
            if(! $user_logged_in && ! empty($field_args['hide_in_registration'])){
                continue;
            }
            if( isset($field_args['js_trigger']) && $field_args['js_trigger'] ){
                $enable_js = true;
            }
            if( isset($field_args['js_triggered_by']) && $field_args['js_show_val'] ){
                $data_js[$key] = [ $field_args['js_triggered_by'] => $field_args['js_show_val'] ];
            }
            // Form fields output
            woocommerce_form_field($key, $field_args);
        }
        if( $user_logged_in || ! $enable_js ) return; // Exit

        // JQuery code
        ?>
        <script type="text/javascript">
        jQuery( function($){
            var a = <?php echo json_encode($data_js) ?>;
            $.each(a, function(b,o){
                $.each(o, function(k,v){
                    $('#'+k).on('change', function(){
                        var cf = '#'+b+'_field';
                        if ( $(this).val() == v && $(cf).hasClass('off') ) {
                            $(cf).removeClass('off');
                        } else if ( $(this).val() != v && ! $(cf).hasClass('off') ) {
                            $(cf).addClass('off');
                        }
                    });
                });
            });
        });
        </script>
        <?php
    }
}

Code goes in function.php file of your active child theme (or active theme). Tested and work.

1) On load, field is hidden.