hoggyrubber,
Baldy speaks the truth..and your sleuthing isn't half bad either. The wire going from the brake switch to the turn signal switch is shown as a 20 gauge white, just like you said. The schematic shows a pair of 18 gauge coming out of the turn signal switch going to a firewall connector..they are pink for left stop/turn and violet for right stop/turn. Stuck in with those should be a 18 gauge black which is taillights.
You must have some type of voltage tester to know the white wire going up the column has power. If neither PINK or VIOLET has power at the firewall when your helper hits the brakes, the chances are that the white wire has broken further up than you can see, or its contact in the mechanism is broken or has fuzz or a candy wrapper on it preventing it from making contact with the other two switch points.
It might be time to think about pulling the steering wheel to get a first hand look. Does the turn signal lever feel mushy or funny when you signal a left or right turn. Have you tried sticking a new turn signal flasher in!
Stuart