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Hello, thanks for posting
Do all the other lights at the rear work? Only the brake lights are out?
A common problem on the Camrys of that year is that the wires inside the insulation of the sub harness stretch and break, this harness comes from the tail/brake lights and runs up along the left trunk hinge to the inside of the trunk on the left side to the tail light failure relay and then into the passenger compartment, the wires usually break somewhere between the hinge and the relay, you'll need to cut the insulation away about a couple of feet and check the wires inside by pulling on them, some of them may pull apart, especially the ground wires which are brown/black, the tail wires are green/white, splice any broken wires together and tape them up to prevent shorts.