You say that your rear turn signal lights work but not your stop lights. If this is correct then your problem is not with the wire that you found but back in the cabin of the vehicle.
The turn signal lights and the stop lights share the same wires back to the turn /hazard switch assembly on the steering wheel.
The power for the stop lights is fed from the stop/hazard fuse through the brake pedal switch and into the turn/hazard switch assembly. Out of the turn/hazard switch assembly it is the same wires to the lights for the turn signal, hazard signal and stop signal.
Check to see if your hazard lights work. They are the same lights and 'share' the same fuse as the stop lights (The hazard/stop fuse supplies power to the flasher unit to operate the hazard lights as well as the stop lights, the turn signal lights use a different fuse to operate the flasher unit). If they work then the brake light problem is with the switch mounted on top of the brake pedal or in the turn/hazard switch assembly. If they don't work then most probably the stop/hazard fuse has blown.
Here is an image of the wiring diagram. I think that it is the correct one
Maybe the wire that you have found, which I assume goes back to the stop/tail lights was run in for another purpose, like a trailer connection perhaps.