My Buick LeSabre, 2000 model, has had the wiper motor replaced 3 times in an attempt to solve this problem. The multi-switch has also been replaced. The rain sensor on the windshield was disconnected after the 3 motors were put in just to eliminate a potential cause. It is plugged back in now.
The problem is intermittent as well. When you are driving, the wipers engage and nothing will stop them.
The car has a little less than 80,000 miles on it.
Well, if the switch, motor, and rain sensor have been eliminated, that makes me suspect that the insulation on the wire between the switch and the motor relay has frayed, and is now touching something metal and completing the circuit. Depending on where it frayed, this can be easy or hard. If it frayed somewhere reasonably accessible, you can wrap the frayed part in electrical tape or, even better, heat shrink tubing to re-insulate it. If it’s not reasonably accessible, you might have to run a new wire - that would be the hard option.
I saw this problem on a GM truck last fall. It turned out to be a bad wiper relay. Check to see if your Buick has one because they are inexpensive and simple to replace.