There are 3 fuses that are in this circuit. In the fuse box on the side of the dash board, check (with an ohm meter!) fuses #12 and #26.
Then, on the left front fender apron, check fuse #8. Not all of these are specific to the rear wiper, but ALL are involved in the circuitry and can have an affect on operation.
There is a switch on the rear window that shuts off the wiper motor if the window is open. Ensure this switch is operating correctly. If it thinks the window is open, the wiper will not run.
Next, in the same box under the hood, there are two relays. A rear wiper up relay and a rear wiper down relay. Check and replace as necessary.
Finally, if you still can't get things working, then you either have bad wiring, or the GEM is bad as it handles and controls all the inputs for correct operation.
There is another relay in the Auxillary Relay Box, but it's for the washer, so you shouldn't have to deal with it.
Oh yea...just because the washer works doesn't mean the switch is still good.