Well it doesn't exactly go "through" the switch, they are simply using it for a terminal block, but I don't think that's correct, either
The 67s were drawn differently than newer If you look at the wire chart on page 8-119, there's only one reference to white, and that is "D4" and "D4A" which comes off the "cold side" of the brake light switch and feeds to pin 7 of the turn signal switch
D4 goes down to the emergency flasher toggle from pin 7. I believe that is an integrated plug on the hazard switch.
The brake light power is pink, comes off (junction) of the hazard flasher, which is fed from the fuse panel