I'm going to label these two gears of interest the "inner" and "hour hand" gear. The hour hand gear is the one with the stem riser that winds up accepting the hour hand. The inner gear meshes on its outside edge with the minute hand shaft and on the small raised inside nested gear with the hour hand's outside edge gearing.

The outside of the inner gear is the same for both the 12 and 24 hour models. There are 45 teeth. Where things begin to differ is on the inside gear of the inner gear. For the 12 hour model, there are 12 teeth that mesh with 48 teeth on the hour hand's gear. For the 24 hour model, there are 8 teeth on the inner gear that mesh with 64 teeth on the hour hand's gear. If you do the math, you can readily see that the 24 hour gear ratio is twice that of the 12 hour model (12/48 = .25, 8/64 = .125).

It doesn't seem like there's any optimizations to this that we can conveniently make. If we attempt to reduce the number of points on the inner gear we have to make its diameter smaller, and it's already got no room to do so given that it has to sit on a spar in the chassis that's a certain diameter itself.