I have partially dissected my wiper/washer pump to clean it up and get it functioning properly again. What kind of grease is that inside where the auger shaft and gear is, and can you still get it at regular auto parts stores? The old stuff was pretty hard, almost like wax. Seems like the design of this was so that the auger would feed the parts new grease as it was used up over the life of the pump.
Chumley

 

Once you get all the old dried lubricant out put in a healthy glob of fresh Vaseline.

 

I used all purpose wheel-bearing grease on my rebuild. The Vaseline might get too liquidly with the heat of the engine compartment, etc.
Good luck.