You really need to isolate the motor from the switch to know exactly what the issue is. The wiper motor can be tested while still mounted on the firewall. This is a cut and paste from a white paper I wrote on how to test the motor. It is best down with alligator clip leads and insulated boots over the clips. Radio Shack has what you would need. (Did I just write Radio Shack???)
Three Speed Wiper Motor Bench or Firewall Four Wire Terminal Test:
Forward (Slow)
12V+ to Red & Brown
Green to Motor Ground Strap
12V- to Motor Ground Strap
Forward (Fast)
12V+ to Brown
Green to Motor Ground Strap
12V- to Motor Ground Strap
Red Not Connected
Reverse (Park)
12V+ to Blue
Green to Brown
Red to Motor Ground Strap
12V- to Motor Ground Strap
Note: If the motor does not move forward initially, try the reverse test, once. If the motor returns to the park position and stops, continue with testing the forward motion. The motor will not move forward if the last power applied was moving the motor in reverse and did not complete the park motion.
Give that a try and see what happens with park. If the motor doesn't park after testing like this, the park disconnect arm may be not making contact inside the gear box cover.
Jim