Yea, I never heard of one either but this one came in a month or so ago. Over the years people have wandered into my store with all kinds of things, large and small. Slot machines, scales, model trains, etc. I think they spot all of the little tools and figure that you can fix about anything.
This one was a little different because it was a longtime friend that brought it over. The cyclometer mounts on the frame of a penny-farthing or hi-wheel bicycle. The cross shaped piece on the top straddles the spokes and as the wheel rotates, each spoke advances the counter. As a big collector of the bicycles, owning many of them, he only had one of the cyclometers until he recently bought this one. When he got it it he saw that it was missing a lot of pieces. It's a good thing he already had one that I could use as a model and see what the missing parts looked like, because there doesn't seem to be anything online about these things.
The main shaft which has a worm gear on one end and a cross shaped piece on the top were missing. The glass lens was also broken. I don't have any pics of that part of the repair but the glass was replaced with a nice fitting pocketwatch crystal which is held in by a soldered retaining ring and plaster. I wish I took more pics.
Here are some views of the replacement shaft that was handmade.