A well known failure mode of the electronic type odometer is a broken gear inside the odometer drive. This drive basically is an electric motor spinning a epicyclic gear that in turn drives the odometer. The speedometer usually remains unaffected.

That's the basics done.
A short while ago, I noticed it was my turn to be the "victim" of a broken gear. So I took the odometer apart, and yes, a tooth had broken off of the little 25 teeth gear.

Then I went looking for replacement gears and found out there are two versions: one with 25 teeth (like I have) and one with 26. But no one would specify when what gear was used and in exactly what instruments.

Obviously, I was wondering why this is, but I couldn't find that out. Only that it was the case with SOME odometers. It didn't seem to matter if the odometer was in miles or kilometres, or what its K-number was.

So I went digging some more. I found here that the 26 teeth gear would make the odomoter run differently. The larger gear would make the odometer go slower by " almost 3%". But strangely, an example was given in mph (speed) and the one thing that gear doesn't affect is the speedometer in the electronic version. With the odometer gear broken, the speedometer will happily keep working as it always did. So that just seemed wrong.

I also couldn't find any basis for that 3% figure. If there were any difference, it would have been almost 4%.

Then I realized that the gearing of the odometer drive is an epicylic gear.
I went on to read about epicyclic gearing ratios, only to find out that the broken gear was the one gear that did not affect those ratios.

Rather counter intuitively, it DOES NOT matter if that little gear has 25 or 26 teeth. Only the number of teeth on the driving gear (on the motor) and the number of teeth on the clear plastic housing (61 teeth to be exact) determine the ratio (together with what part of the epicyclic gear is held stationary).

So for all wondering why there are two versions: I still DON'T know. I do know it doesn't matter which one you replace the old one with. Often, the 25 teeth version seems to be the cheaper option.

Epicyclic gearing