@Frank, It's just me being a bit worried about cutting into anything on my Daily Driver. Just paranoia ...
For the OEM 3rd brake I believe only 2 wires are there
Ground
Brake (Switched connection only while the brake is connected)
Beyond that the license plate light (part of the relocation) needs both of those as it replaces the 3rd brake light, but also needs a wire (Switched on while lights are on)) for the license plate.
My brain says the tail light has 4 wires,
Ground
Taillight (Constant while lights are on)
Brake (Switched while brake is on)
Backup (Switched while in reverse).
All the instructions I've found for relocation to the spare tire mount have the wiring for the 3rd wire needed going to the passenger taillight to splice into the tail light wire there.
That is unless the tail only has 3 wires and somehow the taillight and brake light are on the same wire and it just sends extra power, or some signal to brighten. Not sure how that would work if it did...