There is a "park-run" switch integrated into the wiper motor assembly. When you select intermittent operation, a relay in the Generic Electronics Module ("GEM") powers the wiper motor for a fraction of a second. Once the wiper arms begin to move, the internal switch transfers from "park" to "run", and maintains power to the motor until it completes a full cycle.
In non-intermittent modes, the internal switch ensures the motor always stops in the park position, regardless of when you turn off the power.
If your luck is good, the cause could be just a broken wire or bad connection at the wiper assembly. On the other hand, if your luck is not so good, you might need to replace the motor assembly. You might try one from a wrecking yard, to be sure it's the motor, before buying a new one.
I recommend to heat the plastic cowl piece (the black part between hood and windshield that covers the wiper mechanism) with a hair dryer do avoid snapping the retainers when you try to remove it.