Woocommerce custom fields won't update when I leave them empty and still display

I added a custom field to a single product page for woocommerce in order to show ISBN number for the books I sell. I found a nice guide and managed to add everything as I want. However when I empty the custom field for ISBN it won’t go empty on the site.

I have the following code in the functions.php

// Display Fields
    add_action( 'woocommerce_product_options_general_product_data', 'woo_add_custom_general_fields' );

    // Save Fields
    add_action( 'woocommerce_process_product_meta', 'woo_add_custom_general_fields_save' );

    function woo_add_custom_general_fields() {

      global $woocommerce, $post;

      echo '<div class="options_group">';

      // Custom fields will be created here...

    // Text Field
    woocommerce_wp_text_input(
    	array(
    		'id'          => '_ISBN_field',
    		'label'       => __( 'ISBN', 'woocommerce' ),
    		'placeholder' => '',
    		'desc_tip'    => 'true',
    		'description' => __( 'ISBN.', 'woocommerce' )
    	)
    );
    function woo_add_custom_general_fields_save( $post_id ){

    	// Customer text ISBN Field
    	$woocommerce_text_field = $_POST['_ISBN_field'];
    	if( !empty( $woocommerce_text_field ) )
    		update_post_meta( $post_id, '_ISBN_field', esc_attr( $woocommerce_text_field ) );
    }

Then in the short-description.php I made it so that it shows on the product page. However it still displays the name ISBN10: if it’s an empty field.

<?php
    // Display Custom Field Value
    if (!((get_post_meta($post->ID, '_ISBN_field', true))==”)) {
    //Not empty
    echo '<b>ISBN10: </b>',get_post_meta( $post->ID, '_ISBN_field' , true);
    }
    ?>

So the two problems are I can’t edit the product to contain an empty custom field. And if the field is empty (only possible when field hasn’t been previously contained data) it still displays the field name.

Thanks in advance.

https://wordpress.org/plugins/woocommerce/