I start the car to show it off to a friend and let him hear the purr of the rotary. (1990 GXL). I walk inside my garage for a few minutes while the car warmed up, and when I come outside the windshield wipers are on. I flipped, clicked, spun, and pressed every button around the steering column and they will not stop. I inevitably turned the car off and walked away... What is going on?

 

Wiper switch.

 

could be the switch relay is stuck closed, but that would usually only happen if he had just used the wipers and it is semi uncommon.

what probably is the issue is the parking pad inside the motor has corroded and lost continuity so the wiper motor has no clue where to park and just runs continuously while trying to find it.

in the meantime, you can just pull the plug from the wiper motor to get them to stop.

 

That would also be my guess.