I've done some more poking about as regards the rear washer. It looks like I've got a broken pipe. I gave the rear washer a good burst. As I walked around the car. I saw a puddle under the passenger side door. I gave the washer pump anther good go. The water appears to be coming out from between the vent holes at the bottom of the sill.
Does anyone know exactly where the pipe runs and how to get to it?