Of course I already bought a new (injection molded) gear.

The odo worked when I bought the car, but stopped after about a week.

Turned out to be just a bad solder joint. A resistor was free to move in and out. There was another joint next to it that was suspect, so I reflowed it too.



Odometer works fine now.

 

Very interestesting. Good troubleshooting. I ended up replacing my deteroriated gear but it didn't fix the problem. I'm wondering if something like this was present in mine...

 

Ken, you lucked out... If you had gone in there hoping to solder a loose connection to fix it, the problem would have been the gear.