It seems like it could only be the switch. I've never taken the switch gear off of this car so I don't know how to do it, but if you can get a can of Quick Dry electronic cleaner from your local parts store, stick the straw on the nozzle and shove it up into where the electrical connection of the switch is. Also spray the moving parts. Keep a towel on the floor of the car to catch the crap as it drips out.
It might work and save you a couple bucks.
If it doesn't work, UNPLUG the switch and drive around and see if it does the same thing. That would prove or disprove the switch.
I do NOT know if there is a relay on the system.
B