I added custom script:
wp_enqueue_script(\'functions\', get_bloginfo(\'template_url\') . \'/js/functions.js\', \'search\', null, false);
I
You could avoid hardcoding the full path by setting a JS variable in the header of your template, before wp_head() is called, holding the template URL. Like:
And use that variable to set the background (I realize you know how to do this, I only include these details in case they helps others):
Reset.style.background = " url('"+templateUrl+"/images/searchfield_clear.png') ";