Important: Since version 3.0.0 this is NO longer required. You can display/hide the search icon in the menu as explained in the docs here: http://total.wpexplorer.com/docs/header-search/
By default the menu search icon is disabled on header style 2 because it’s added directly in the header as a form. However, you can easily enable it via a function in your child theme. Simply add the following to your child theme’s functions.php file:
// No code needed anymore...
Result
As you can see you will have both the search icon in the menu and in the header, so simply go to Appearance -> Customize-> Header -> Search to disable the form in the actual header area.