WooCommerce Taxonomy Archive with Live Search

<?php
/**
 * The Template for displaying products in a product category. Simply includes the archive template
 *
 * This template can be overridden by copying it to yourtheme/woocommerce/taxonomy-product_cat.php.
 *
 * HOWEVER, on occasion WooCommerce will need to update template files and you
 * (the theme developer) will need to copy the new files to your theme to
 * maintain compatibility. We try to do this as little as possible, but it does
 * happen. When this occurs the version of the template file will be bumped and
 * the readme will list any important changes.
 *
 * @see         https://docs.woocommerce.com/document/template-structure/
 * @package     WooCommerce/Templates
 * @version     1.6.4
 */

if ( ! defined( 'ABSPATH' ) ) {
    exit; // Exit if accessed directly
}

// Register and enqueue live search script
add_action('wp_enqueue_scripts', 'fivetwelve_live_search_script');
function fivetwelve_live_search_script() {
    wp_register_script( 'live-search', get_stylesheet_directory_uri() . '/js/live-search.js', array('jquery'), '1.0.0', false );
    wp_enqueue_script( 'live-search' );
}

// Add the live search inputs above the products
add_action( 'woocommerce_before_shop_loop', 'fivetwelve_live_search' );
function fivetwelve_live_search() {
    ?>
    <div class="live-search-wrap">
        <!-- These filtering fields can be hidden with CSS. They are populated via query strings in the URL, sent from the intake form. -->
        <form id="live-search" action="" class="styled" method="post">
            <fieldset>
                <!-- Create an input field that looks for the "var1" query parameter in the URL -->
                <input type="text" class="text-input" id="filterVar1" value="<?php echo $_GET["var1"]; ?>" />
                <!-- Display the returned count of elements matching var1 -->
                <span id="filter-count-var1"></span>
                
                <!-- Create an input field that looks for the "var2" query parameter in the URL -->
                <input type="text" class="text-input" id="filterVar2" value="<?php echo $_GET["var2"]; ?>" />
                <!-- Display the returned count of elements matching var2 -->
                <span id="filter-count-var2"></span>
            </fieldset>
        </form>
    </div><!-- end .live-search-wrap -->
    <?php
}

wc_get_template( 'archive-product.php' );