You should follow Ranger's advice anyway. The added wear on the wiper motor from being on all the time (if I understand correctly), not to mention the micro-fine scratches you are invariably putting in the windshield are reason enough.
My 1992 DeVille has this same problem. If I use the windshield washer or turn on the wipers, they won't shut off. Also there is no intermittent or MIST speed. When I turn the wiper switch to OFF they keep going but when I shut the car off and then restart, the wipers park and stop. It began gradually a while ago - when I would use the washer, the wipers would not automatically shut off. I would set the switch to MIST and they would keep going on LOW speed for a while but eventually they would go into MIST mode and at that point I could shut them off. Now they will not stop until I kill the motor. The local dealer says the module is not available, on indefinite backorder. Plus I am not certain if it is the switch or the control module.
I understand that I can unplug the wiper motor under the hood but here in Florida where it rains on/off unpredictably that is inconvenient. What do you think? Is it the module or the switch? I heard that if the wiper fuse is removed and the blades keep going, then it is the module. If they stop, it is the switch. Any truth?
I am considering installing an inline toggle switch, basically hot-wiring the switch so I can kill the wiper motor manually while driving. Would this work? If so, which wire should I interrupt?