2002 Pontiac Sunfire

Is the 3rd (high mount) brake light working?

NO, I don't believe there is one.

Yes, there is. It's required by law.

yes your right. It don't way.

It appears your saying the high mount light doesn't work.
Everything your saying is not adding up correctly.

The lower brake lights and turn signals all run through the turn signal switch so this would be the likely suspect for your problem, however the high mount does not follow that patch and works directly from the brake light switch so your going to have to do some testing. Test for power coming into the brake light switch constant and going back out when the brake is applied. You could have had issues with the high mounts before this.

Where is the signal relay located. I will try that first.

That would have nothing at all to do with brake lights.
It's mounted to a bracket above the brake pedal.