[petek]

Might be a bad ground on the wiper motor or it might be some sort of weird short or miswire to the wiper motor.

I'm guessing that the wiper motor, while sitting in it's park position, is receiving a brief surge of electrical juice on either the slow or fast terminal. All it would need is the briefest burst of energy to cause the motor to rotate ever so slightly off of the park position. Once the motor has spun off of the park position the motor would continue to rotate until it came to a rest in park once again.

Try putting a voltmeter (analog would be best in this case) from the ground on the motor to the slow input and toggle the lights. Then do the same for the fast input leg. An analog voltmeter's needle will move if there is any voltage being applied while the light switch is toggled. (A digital voltmeter or DVM may not show the quick burst of voltage because the meter needs a little bit of time to measure the voltage.)

Another idea... disconnect the slow speed leg and see if the wipers still move when the light switch is toggled. Then try the same with the high speed leg. Should be able to get the problem isolated to a single leg this way.

Sure is a weird one!