I've got a 1992 Camry SV21 Automatic.

It's slow to change gears going up, but seems fine when down changing. Like it gets stuck in a gear for a couple of seconds before it changes up.
Is this just due to needing a trans oil change, or is it something else?

Also sometimes when I take my foot off the accelerator and just cruise before I brake at lights, the RPM will bounce. What could be causing this?

 

Check the fluid level and condition.

What happens to the RPM with the car has finally come to a complete stop. Still bounce, stable, etc?

 

Doing a trans oil change this weekend, thanks.

RPM is steady when the car is stopped. It stops bouncing if I brake or accelerate.
It only bounces sometimes though, not all the time.
On rare occasions it will bounce when I turn the car on, I just turn it off and back on and it's fine.