When enabling JEI/REI synchronized search, it's very confusing which text field now has priority since there are two search boxes simultaneously. We could instead hide the AE2 search box if JEI/REI synchronized search mode is used and simply use the text entered in REI/JEI's own search box for filtering the terminal. It's easy to implement and makes it clearer which search field is to be used.

In this case, the "auto" version of the JEI/REI seach box should also be re-considered. Auto-Focus might be better left to JEI/REI themselves.

Additionally the tooltip of the search mode buttons should be expanded upon to explain that "Auto" refers to auto-focusing the search textfield whenever the terminal is opened.