This may not be what you expect, nor was if for me, but it works (no mouse required)... (btw: I've just started using Terminator, and so far I like it)..
A way to do it is to simply do this:
* If your active cursor is already in the _Find box_ , just keep pressing `Enter` for **Next**.... and for **Prev** , press `Tab` to make the `Prev button` active an then just keep pressing `Enter`... the `Prev button` stays active, so it locates backwards each time you press enter..
* If your current active cursor in in the window body, just press Ctrl+Shift+F again, to get you back into the _Find box_ , then just press Enter (next), or Tab, then Enter (prev)..
Also, you can switch between buttons, to reverse the search direction, via the Left and Right cursor(arrow) keys (I find that easier than Shift-Tab) ...