The washer pump is always hot on one leg (white) from the fuse block. Activation of the motor is accomplished by grounding the other leg (pink). So if the pump is running the pink leg is connected to ground. This is normally supposed to be the case when the WASH tab on the MFS stalk is rotated CCW. Doing that also runs the wipers on low for a few sweeps.
If just moving the wiper speed select part of the switch - to LO/HI/MIST - makes the pump start running, it would appear that you have a ground fault in the negative leg (pink lead) of the washer circuit. But, because it only happens when the wipers are turned on, that would seem to indicate that the problem is in either the switch or the pulse control module (if you have intermittent wipers) - and not in the interconnecting wiring.
If you have pulse wipers, isolate the problem to either the switch or the module like this;
Turn ignition to RUN and turn wipers on - so that pump is running.
1. Pull the connector on the switch side from the pulse module. If the washer pump
stops... the switch is bad. If the pump keeps running:
2. Pull the connector from the wiper/washer side of the module. If the pump stops...the
module is bad