To use an illustration I've seen on the sister/deadbeat older brother site to describe celestial gears:
The inner gear would be the Northern star system, rotating one direction, and it's surrounded by the Southern: the stars rotating the other direction, closer to the edge. I'm assuming something like this is accurate: if there was only one such outer 'gear' then at some points there'd be no stars in the sky, which is clearly wrong.
Can anyone describe the stars in the outer gears? The inner gear is understandable, we can observe that star system, but what of the outer? Are they the exact same set-up of stars repeated three times? Is each one just a fraction of what we think of as the southern star system?
It doesn't seem entirely clear as to why, for example, we've never observed stars rotating around three points in the sky: the inner, and then two gears of the outer.
The wiki doesn't seem to dedicate any time to the topic, and I haven't found any actual explanation of gears via the search function. They're just appealed to with no description.