Stu,
Found the guide (which is excellent, although referring to magnetic instruments rather than chronometric). I think the key lies in this section:
The ?old? style odometers work by friction trying to turn all the odometer wheels and then a restraining clip underneath the wheel prevents motion except at certain times. The drive gear is keyed to the shaft and there are keyed washers between each of the wheels. The wheels themselves are not keyed and can turn freely. As the drive gear turns, it turns the shaft. The shaft turns the washers between the wheels. By friction, the wheels try to turn, but the clips prevent turning. The restraining clips underlie two adjacent wheels, so one wheel can disengage the clip under the next wheel to the left. The left and right edge of each wheel have a thin metal edge with notches. These notches engage the clips. On the right side of each wheel the edge has ten notches. The left side of each wheel has one notch. When looking at two wheels, as the right wheel turns one entire revolution, it disengages the clip under the left wheel once. The right wheel moves ahead by one notch, then the clip re-engages and prevents further forward motion until again disengaged.
So I need to look at how the clips are engaging and disengaging.
Fascinating stuff!