I'm using Firefox right now. When I highlight in the bar and press tab, ONLY when the drop-down bar is showing, it moves the cursor down one to Amazon, which is not my default search engine, but the first one alphabetically.

So that doesn't work.

I also don't want to search my default search engine. I want tab to search for the panoply of websites that the omnibox will search. When I start typing ebay, I want "tab to search ebay".

I know I can set them up manually (a pain, but might be worth the investment to avoid the google overlord), however, I still don't get the "tab to search blah" function with a keyword. I have to type the keyword exactly -instead of having tab function as autocomplete- then space for my query.

What I want is omnibox tab to search.