Audi rear wipers are famous for failing and it is due to corrosion through washer fluid leaking into the motor. I would say gears are blocked, because grease has mixed with washer fluid. Remove trim, remove motor, open motor housing, clean, install additional o-ring (so it never mixes again), use new grease (water resistant), close housing, test. If motor circuit is wet, maybe it is broken.
The two wires you measured always have 12V, the other two are trigger from control unit, you cannot measure it with multimeter.