Looking at the wiring diagram, the wiper motor is supposed to ground through the body.
The wiper motor should have a three wire plug; Green, Black, and Red.
If you hook the Red to 12V and ground the body of the motor, it should spin.
I think hooking the Green wire to 12V would make it run on the low speed, but the motor also has an internal "Park" switch so it may be an intermittent low.
My first guess would be to check and clean all your connections. Also, try hooking up a jumper cable to the body of the motor and grounding it. It may be the ground that's causing the problem.
1973 VW Karmann-Ghia first car
2009 Challenger R/T 6MT, Flowmaster, inTune daily driver
1977 CJ5 304, 3MT - under construction
And many in between!