I have a 94 sunbird SE. 3.1 V6 matched to a 5 speed. The car has been working great until recently.

Whenever i put the car in reverse, the reverse lights come on (but are very dim). The odd part is that when it is in reverse, most of the voltage is going to the center mounted stop light, but the rear left and right stop lights are also dimly lit.
To summarize, when the car is out in reverse, the center mounted stop light shines bright, but the tail lights and reverse lights are dimly lit.
I checked all the fuses, and they are all fine. I pulled the fuse for the reverse lights, and the problem disappears. Put it back in, and the same thing.
Any ideas? I think it's a short, but where? Other than this, the car works fine. Lots of power, never stalls.

Does the power go throough the fuse panel before hitting the computer or vise-versa?

Try checking your grounds... could be loose? Also may be a short in the fuse itself.. try replacing the fuse with a brand new one

i had a similar prob, it was my reverse switch on the trans.
it was a bit loose and dirty. cleaned it and re-tightened and
that solved the issue as stated.

LOL my 93 Sunbird would do this... Every time I put the car in reverse my fuse would blow and I wouldnt have turn signals.

Turns out that my wire was stripped near the sensor and was grounding out on the transmission. I just unplugged it and didnt have back up lights anymore for a long time.

Yours might be somewhere else but you definalty just have a short somewhere. Time to trace some wires.