On our site the search bar in the header seems only to search posts/post content. Nothing appears in the little AJAX popup below the search form when a word is entered into the field.
Despite that, the 8theme Search Form widget (which is placed into the main sidebar and currently that sidebar only appears on the checkout page and individual blog posts) DOES show products in the AJAX popup.
How can we have these two search forms work the same way?
Site URL: hidden Theme version: 2.10.0 WooCommerce version: 2.6.9
Unfortunately, there is no such possibility. Sorry.
In this case, you can edit header.php file and use customization of the default theme files in the child theme. Please read how to create the child http://www.8theme.com/demo/docs/legenda/index.html#!/child_theme
All available theme search settings can be found in Theme Options > Search.