In Firefox desktop browser, Ctrl + k will focus the address bar so you can type in a web search. I've noticed same keyboard shortcut does nothing in the Show All History interface.
Ctrl + k is in my muscle memory, and I sometimes invoke it in History search (to no avail!). I think it would be very handy for Ctrl + k to focus the Search History box in History search in the same way it already focuses the Address Bar in the browser proper.
That's it - that's my suggestion!