3B has it right. The white wire attached to the brake light switch feeds into the turn signal switch.

Check for 12v at the turn signal switch end of the white wire when the brake pedal is pushed.
If no 12v, fix the wire. If you have 12v fix or replace the turn signal switch.

Here is a partial wiring diagram showing the brake light and turn signal circuits for your 64.

Last edited by Bill Hanlon; 05/15/2025 1:48 PM. Reason: new info

'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.