I'm going to start off by replacing the directional switch in the column. I guy I met at a show yesterday said he had a similar problem and it was the directional switch.
Yeah, weird things can happen at the directional switch.
If this helps illustrate my comment: A guy told me in traffic one day that the left rear brake light wasn't working on my '67 Satellite. Turns out the screw holding the directional switch stalk got loose inside the steering column. The force of gravity on the loose directional stalk moved it downward close enough to the 'Left Turn' detent, that it cut power to the left tail light but ONLY WHEN BRAKING. Weird but true. All I had to do was tighten the stalk screw and the problem was fixed.
Best, - Art