Well, if it were mine, I'd unplug the pump and see if the issue stops, which I can only assume it would unplugged

Then I'd see if there was 12v coming from the wiring going to the pump, when the truck is 'on', but you aren't pressing the switch. Which indicates it's getting power when it shouldn't.

Then I'd unplug / remove the switch, and again check for power at the pump wiring. If it goes away, I'd highly suspect the switch as the issue..
Then I'd look up the part for the switch and replace it...

Or, more likely, just buy the switch and swap it since you don't want to take it apart 2x.

 

The BCM provide the signal that closes the relay for the pump. Does the washer provide full force when you push the wash button? If not you may have a bad relay or a bad ground for the pump. Pulling the FRT WASH fuse should stop the pump until you find the problem.

 

Thanks for the replies guys. Yes, the washer provides full force when I push the button. Would the BCM also provide signal for the headlights? The reason I ask is I think there's an electrical gremlin that's causing my issues. The high beam headlights and the fog lights will come on sometimes when they shouldn't be on. They will be real dim but they will be on. Also both passenger side doors will not lock with the keyless entry or the unlock switch in the vehicle. Could the BCM be causing all of these issues?

 

Sounds like your gremlin is probably a bad ground. The fog lights, headlight, & the washer pump share a common ground. Follow the black wire from any of these to where it attaches to ground, make sure the it has clean metal under the screw.
The door lock is probably a separate issue. Does the passenger door switch lock the door? Does the left rear door lock work at all? The same relay controls both back door locks, if one side works then the problem is in the wiring to (or inside) the doors.