My neighbor had the same problem with his Nissan Altima. I went over and check the wiring to the affected side (left rear brake light/parking light) and sure enough, all of the ground wire connections were corroded where they were connected to the tailight assembly.
If the lights will work independently of each other, but fail when both are used at the same time, it is probable that the ground connection is corroded to the point where it will not conduct enough juice to support the operation of both lights at the same time.
Check for corrosion on the contacts inside the bulb sockets, too. Once you scrape/clean them, a little white lithium grease will help prevent corrosion in the future.
I cleaned and tightened the ground wires and all his brake/turn signal/parking lights work properly now.
You did not say if this happens on just one side or both, but check this and let us know if it fixes your problem.
Good luck - Paul
Tuesday, April 17th, 2007 AT 9:09 AM