If you are having to restring, you may want to fix the pully shaft, as it is usually loose where it connects to the small pot metal gear. If it is loose it is pretty easy to pull it out and have the gear and washer drop out when doing the restringing.
Understand that when you remove the shaft, the gear drops out along with the stop washer. I usually remove the 2 small screws that hold the small pot metal frame to the tuning capacitor. This way you can work on it easier. I used to try crazy glue, but it always dried before I set it properly. So now I distort the end of the shaft where it goes into that pot metal gear. I use a heavy pair of Dikes and just put 2 small crimps onto the end 1/8 inch apart. Then you can put the washer in place and push the shaft into the gear . Tap it in and it should hold fine. You then need to reset the spring loaded gears so the assembly doesnt have "gear slop"
But if the shaft doesnt seem that loose, you may not want to tackle it, just be careful to not pull it out on the restringing. You may want to see if it may have come out before and somebody else put it back in. Easy way to see is check that the spring loaded gears are still spring loaded.
The procedure is hard to explain in words. I may put a little tutorial together to explain how to do this as well as show pictures.