You may want to re-seat your gtia chip as well, which reads the trigger button. About your question on the multimeter, yes it's a continuity test what you could do, but I doubt that's the issue if all of your joysticks fail equally.
10 ? strig(0): goto 10
That's your basic trigger tester. if the value changes when pushing the trigger, you're good. use strig(1) for the other port.