Big Mistake!
I had an analogue joystick. I did try it with the GBA and found that it worked.
BUT... I only tried it in one direction. Later I would discover that this whole control system was useless.
My instincts were already telling me that this wouldn't work, but after I tested it and had a positive outcome, I kept on going with a flawed design.
(This image is the Arduino control board, cut in two and set at two different heights. It would have been brilliant if it had worked.)