I am about 99% certain Turrican 2 supports the second button on my Arcade Evolution joystick. I'm not a huge gamer but a few other games I've tried do, as well. Actually took some getting used to, since all I've ever had is one-button joysticks in the past. Maybe you might want to discuss this project with AmigaKit, for their various new joystick models they're working on?
Nevermind, I'm sure they'll chime in on this thread soon enough.