Comment 1 for bug 310217

When the search box is hidden (either because you've removed it from the toolbar or you've hidden the toolbar), the browser uses the "default" search engine. There are two problems here:

1) There is no way to change what the "default" search engine is (the whole "default" search engine thing is mostly vestigal, left over from the old days, but there are a few remaining places, such as here, where it still gets used). This is bug 331105.

2) The search box shouldn't even be considered as hidden for the purposes of search engine selection when you're in full-screen mode with the toolbars set on auto-hide, since auto-hide represents temporary hiding and not the result of you trying to remove the search box. AFAIK, there is no pre-existing bug to deal with this particular case.