The electrical connection is really weird. Only two wires.
If the front washer is activated, the relay feeds positive to one terminal and negative to the other and the pump spins one way and water goes out of one pipe.
If the rear is activated, the reverse polarity is presented to the pump, the pump spins the other way and water goes down the other pipe.
I'd suggest, first step, remove the pipes from the pump and see if you get flow out of one or the other depending on which end you are activating. That'll tell you if the issue is the pump or the pipes.
Next, if that doesn't work, check what readings you get on a multimeter. If you don't get the reversed voltages depending on switch activation, then I'd suggest the relay/ control mechanism in the stalks is duff.