[ACK]

Attached is the '64 light schematic, the light switch harness doesn't look like it's matching your harness. Also, here's some things to try ...
1. Disconnect the light harness at the dimmer switch on the floor. Turn on the headlights, if the brights indicator is on, I'm betting a bulb behind the dash is in the wrong position.
2. Pull the orange wire at the brake lamp switch. If the brake lights are still on, double check the wiring.

Good luck and give updates as you go along.