With the lights off both rear brake lights work correctly, with the lights turned on the left rear brake light shines bright as if I were pressing the brakes while the right one remains dim as it should untill I press the brakes. What would make the left brake light stay bright and not dim. The car is a 1997 camaro, thanks!

 

If you have not already tried it, replace the bulb. It may be that the filliment inside the bulb has broke and became attached to the tail light part of the bulb.
Hope this helps.