Rear quarter windows

You don't have to completely depress them but lower both fronts and rears a couple inches so the top coming down doesn't put pressure on the bearings. Once the top is up, you can roll them up completely.

If you're having trouble rolling up the rear windows, your switch may be bad. It's VERY easy to change it out and the switch is only $20. Don't bother cleaning the contacts on the old one - it's a temp fix aside from just replacing them. And replace the pair rather than just one at a time.

Good advice because the roller guides become brittle over time and pressure might cause them to prematurely fail. On my '91 I had to replace the plastic rollers for those rear windows because the window would not go up all the way and the mechanism came off the plastic rollers. . They become brittle over time and chip apart.
There are replacements online but not an exact fit. Had to modify them a little.

The rear quarter windows are not lowered before opening or closing the convertible top. The top mechanism should work independently of the windows. However, it's always a good idea to double-check the owner's manual. As for the glitchy power window switch, it's understandable that you'd want to leave the window up if you're having trouble with the switch. But if the window needs to be lowered for the top of the cabin to work properly, the switch may need to be inspected or replaced.

On a 5th Gen Celica convertible, the windows are supposed to be lowered whenever opening or closing the top - per the convertible supplemental owners manual. Not sure about a 6th Gen, but I would think it would be the same.

Why don't you replace that rear window switch on yours, if you are thinking the problem is with the switch?

Not sure how readily available those rear window switches are on a 6th Gen Celica. If difficult to find, there is a 6th Gen Celica convertible out in the salvage yard by me. It is pretty well picked over, but that switch may still be there. If you want to replace yours and can't find a replacement, if you want me to check if that salvage convertible still has it's switch in it, let me know.