I don't know about the sidekick auto, other than I drove my Sister's a few times.
It was a three speed. No overdrive.
It desperately needed an OD.
When I first read your post, I thought about the internal workings of an auto.
The GM autos I have done, and I think most others, don't have "gears" except in the tail shaft section.
(which I never fooled with).
The rest is a series of clutch packs, the valve body down below, and of course the torque converter.