I understand that, but what I don't think that makes much sense is the Search field that a e-commerce template has doesn't search the products. It's a highlighted field that leads the visitor to something that it doesn't do.
I have done my own solution... which is to not use the Joomla search button.
1) installed j2store search module - published in a hidden location for all pages.
2) switched off the joomla search module with the magnifying icon next to the menu,
I created my own module, copied the code for the "Magnifying glass" and it's assigned to the menu location. you can also use an image but the icon is better and does not pixelate. I also added a custom class.
3) I bought Engagebox component which allows popups/lightboxes. And I assigned the j2store search module to be activated the moment someone clicks that Magnifying Glass icon with that class.
http://www.liquorbar.sg