Just to give you a heads up today I swapped out my old washer pump with a new one from the parts store. Works great.
And for ****s and giggles I decided to take the old one apart.
Turns out the armature for the motor was seized up big time. Nothing was turning.
But a little WD-40 and some turning got it freed up again. I had to take the top off though.
But I think I see why, as it looks like it had a leak so all that washer fluid caused some corrosion. And it even corroded the outside of the pump so it's probably gonna leak, maybe I'll find some other silly use for this pump. (hint: water pistol gun

)
Mind you it's much easier and worth the avoidance of hassle to just swap the old pump with a new pump as opposed to fixing your old one. I just had some time to kill and thought "what the heck".
Also I was wrong about removing the wiper pump motor. I actually did have enough (but just barely) clearance to pull the old pump out and reinstall the new one w/o the wiper motor removal.
AC Delco 22049374 is the part number of the old pump in case you need it.