Left Rear Turn Signal/Brake pedal gremlin

[Stickle]

2003 Tahoe, got an occasional fast signal (like a burnt out bulb) when indicating left. It came and went for about half a year, then became more frequent. Eventually the rear left stopped working entirely. Fuses and bulbs all checkout fine, changed the column switch out and the flasher module . No apparent power to the socket (not burnt/damaged at all) and no power to the trailer connector either. Where the gremlins get interesting is that once in a rare while the signal will perform normally if, while the left signal is on, I hit the brake pedal. Intuitively I figure there must be some wire up under the dash or linked to the brake switch at the pedal. Anyone have any ideas?