can't tell from your picture if your payout counter is electrically or mechanically stepped, but in any case that microswitch is typically used for "coin out" meter which is not in all versions of the machine. Some casinos had external meters they would wire the switch to.
as the coins ride around the pinwheel and eject out the front of the hopper, they go under a roller on a pivot arm. If you have a mechcanically stepped unit, the other end of the arm is a linkage down to the back side of the payout counter unit.
in an electrically stepped unit, the pivot arm operates a couple switches and the payout counter steps via a solenoid (coil with plunger in it) that the switches power.
your hopper agitator is shot ... that's the black star-shaped thing in the hopper that mixes the coins as the hopper spins. It doesn't matter much unless it's gooey and getting the coins gunked up, but if you feel like getting a new one, people sell them on ebay for around $14... search for "bally hopper agitator"