OK. So how technical do you want this explaination to be?
The "skinny 6" is there for the cogs on the digit wheels that allow the next power of 10's wheel to advance one numeral for each complete revoloution of the wheel to it's right.
For the operation of main odometer, on each digit wheel to the right of the numerals are 20 teeth around it's perimiter. To the left of the numerals is one single tooth, Between each of the wheels on a counter shaft is a smaller cog with 8 teeth, alternating wide and narrow. The location of the shaft with these smaller cogs happens to line up with the 6 numeral on each of the digit wheels.
In most cases, all of the wheels on the main odometer have the narrow 6. It is possible that on some speedos that the 10k's wheel could have a fat 6. The speedo shown is from a 64 220SEC and has a fat 6 on the 10k's wheel. I know that on most of the speedos that I had worked on the same skinny 6 wheels were used in all positions.
When the tooth cut next to the 6 rolls past the smaller cogs, one of the wider teeth drop down into the slot and advances the wheel to it's left 2 teeth, the wheel is then locked into place by the flat area around the rest of the perimiter contacting between two of the wider teeth of the cog wheel.
The trip odometer operates on the same basic principal but the reset function, of course, makes it more complicated.
Because the counter shaft with the smaller cogs is located above the main odometer and below the trip odometer the single tooth cut in the trip odometer wheels is in a different position. It is there, just harder to see because it is hiding in the open mouth of the 3s (if you look real close at the 3 on the trip odo in the photo Craig posted you can see it) so none of the numerals on the trip odometer wheels needed to be narrowed.
When the odometer stops working it is almost always because the grey metal wheel to the right of the 1's wheel has worked loose from the shaft that all the wheels rotate on. The brass gear to the right of the assembly rotates the shaft one turn every mile (or KM on metric odometers). The grey metal gear is a press fit onto that shaft, the plastic wheel spin free on the shaft with the white plastic cogs on the counter shaft holding them in place.
Al