I've got a car coming my way for a short list of small minor issues to fix. One of the problems is the wipers won't park properly. It's been over ten years since I've addressed this problem and I can't remember the fix.

replace wiper switch

Check to see if it has intermittent wipers. Replace the relay if it's missing. Then make sure the ground is in place.

Mine won't park unless I shut them off within just the right range from the bottom of the stroke. I don't have intermittent wipers (although I'd like to). Is it really certain that this kind of thing is the wiper switch? That's easier than a problem with the wiper motor.

make sure there is power on the park circuit of the motor.
could be an issue with the park points in the motor as well. hope that helps

mine happened when one pin in the intermittent relay slipped and wasn't making contact. IIRC, it was the grnd from turn signal assm. Possibly white w/ brn strip???