So I'm using a custom Genesis child theme. I've created my own PHP file called showcase.php and placed it in my custom child theme directory.
This file is located at: /public_html/wp-content/themes/mycustomtheme/showcase.php
This file is included via a hook:
document.getElementById("ED-quicksearch").style.backgroundImage = 'url("/wp-content/themes/mycustomtheme/images/quicksearch-bg-tucson.png")';