Joe: Diagram below shows how the "bell style" turn signal switch was wired in my '57 GMC. I believe that Chevys were wired the same, including earlier models, as long as they shared filaments in the rear lamps for brake and turn indicators. The white wire is the same as your white wire coming from the brake switch. Ignore other colors on my drawing unless they happen to agree with yours.
The top part of the drawing shows the switch in the "off" position. The center part of the drawing shows the switch in the right turn position and the bottom part of the drawing shows the switch in the left turn position. The yellow pieces represent sliding contacts inside the turn signal switch and the black circles are fixed contacts with wires attached.
Hope this helps you to understand how the switch works and solve your problem.
'57 GMC 102, Original 347 V8, HydraMatic, 3.08 rear gear, added A/C, disk front brakes, HEI, AFB carb, '98 Honda Black Currant paint. T-boned and totaled 10/12 '52 GMC 152 Stake Bed, Original 228, SM420, added A/C, HEI, disk front brakes, '67 Chev 3.55 rear gear. Gets used as a real truck.
