According to the electrical manual I have for the 97, both left and right brake light grounds splice together in a bundle right behind the license plate if you have ABS, or mid driver's side wheel well w/o ABS. The tail light wiring, license plate light wiring, and turn signal wiring grounds splice into the same common ground wires. The wires are white with a black tracer. It looks like they enter the cab on the floor board somewhere in font of the driver's seat and then go into a plug. From there it goes to another splice near the kick panel fuse block where the wire for ground from the cab mounted stoplight come in. The whole thing grounds near the kick panel fuse block. For some reason, something is deciding it likes being grounded through your right rear brake light when the lights are on. You should not have any voltage at either green/white (the hot side) wire going to either stop light without the brakes on. I would get a voltmeter and see which side of the brake light is getting that voltage. Do both brake lights work? If you pull the right brake light does the left then illuminate with the lights on? Does the cab brake light work? Pretty bizarre.