Customize WooCommerce product structured data schema ean / identifier_exists

I am using this snippet to display ean value for gtin in Woocommerce's product schema:

add_filter( 'woocommerce_structured_data_product', 'filter_woocommerce_structured_data_product', 10, 2 ); 

function filter_woocommerce_structured_data_product( $markup, $product ) { 
if ( empty( $markup[ 'gtin8' ] ) ) {
    $markup[ 'gtin8' ] = get_post_meta( $product->get_id(), 'ean', true );
}

return $markup;
}

This works but I need to set "identifier_exists" markup to products that don't have the custom field ean set. How can I modify my snippet to show the ean value in the markup if it exists, and add the identifier_exists attribute = false to products that don't have an ean?

Try the following:

add_filter( 'woocommerce_structured_data_product', 'custom_schema', 99, 2 );
function custom_schema( $markup, $product ) {
    $value = $product->get_meta( 'ean' );
    $length = strlen($value);

    if ( ! empty($value) ) {
        $markup['identifier_exists'] = true;
        $markup['gtin'.$length]      = $value;
    } else {
        $markup['identifier_exists'] = false;
    }
    return $markup;
}

Code goes in functions.php file of the active child theme (or active theme).