Hi garahamlinc0ln, thank you for trying Bad Mood! By right trigger, do you mean the right joystick or the RT/RB button? Also, are you running the PC or the mac version of the game? I never saw this issue before, so if you have more details it would help a lot, thank you!
So when you start the game as the good guy for instance, your are constantly shooting even if you don't touch the gamepad ? This is really weird, I am also running the PC version of the game and I never had this problem (and you're the first one to report it). Maybe it's a bug of Unity 5.3 that appears on on some configurations, therefore it will automatically be fixed in a next update. Just to try to understand, what is your PC's configuration ? Thanks you.