I figured it was a long shot asking about a parking meter on here but that's ok. I found a Facebook group that looks like it might be helpful. The admin seems to know his stuff, so maybe I can get some accurate info. I really dislike Facebook for technical info. I much prefer websites like this.

My wife and daughter went to a Girl Scout meeting last night so that gave me a chance to play around with the meter a little bit. I think I have a better understanding of how it works now. When you insert a coin into the slot, a lever is pushed out and makes contact with a gear. That gear is connected to the timer mechanism and the warning flags. When you turn the handle, the gear is turned and it winds the timing mechanism. There are only gear teeth on part of the gear. That gear seemed to be out of sink with the flags. After taking it apart and putting it back together a bunch of times I figured out how it was all supposed to work together. At least I think I figured it out.

I see two issues that I'm going to have to work through. The first issue is that the timing mechanism works when the unit is laid down on the bench but when you stand it upright, it stops moving. I'm guessing there is an adjustment for the main spring tension. It doesn't look like the spring is wound very tightly. The second issue is that when you turn the handle with a coin in the slot, the lever locks up at the end of its travel and doesn't return to the neutral position. After years of service, the coin mechanism has some slop in it where it attaches to the handle. This isn't allowing the coin mechanism to turn as far as it should to release the coin and reset itself. The handle and shaft are one piece and the coin mechanism is held onto the shaft with a roll pin. Maybe drilling it out for a slightly larger roll pin will tighten everything back up? If not, there is a mechanical "stop" that I might be able to file on which would allow the handle to be turned a little farther.