1998 Lumina - When the turn signal is on, either for the left or right, both rear signals as well as the high stop light blink. As soon as the brake pedal is depressed, the turn signals stop blinking and the brake lights come on. I have replaced the turn signal switch in the steering column but this didn't correct the problem. I had thought it could be a bad ground but am unable to locate the ground for the rear. Any suggestions?

Welcome to AF. Start looking for bad grounds in the affected circuits. You may need a good wiring diagram for this.

I've checked every ground I can find. Ran a test wire directly from the battery to the grounds on the tail lights. Still the same thing. Not sure where to look next.

Without seeing the car, the only other thing I can think of is does it have a trailer wire harness or hitch.

No it does not have a trailer light harness. One thing that I did notice is that the running light come on when the brake is depresses and the blinker is on. I pulled the fuse for the DRLs and the running lights went out but the original problem remained. I'm stumped!!!