For a full brake light problem diagnosis:
Not sure. I followed the wires as suggested. I also replaced the flasher unit and they started working.
White wire at turning switch plug must get 12 volts when giving brakes. If not, problem is on pedal switch. If yes, problem is turning switch.
ALTHOUGHT, once got a similar problem and it was the wire itself broken down the cover at the turning switch harness, just right after the pin. Turning switch itself was still good. I cut the wire, splice new terminal and done.
NOW, you say is just one side... then it could be turning switch problem or related wires ( This is the reason I mentioned the back up history I just wrotte up fixing a rear brake problem, being sometimes just one wire ). Brake pedal switch is correctly working.
HOWEVER, being you have blinkers and hazzards and these light shares same wiring than brakes which are dark green and brown as you mentioned, this discards the wiring including turning switch harness, the problem is definitely the turning switch, maybe just the canceling cam system.