1964 galaxy brake light not working

No, since the one brake light is working that tells us the switch is good. Inspect the bulb socket and the wiring going to the socket. See if you have power and ground at the socket. You can use a 12 volt DC test light or multimeter for that. Does the taillight on that side work? If so you have ground. This is a two filament bulb. One filament is for the taillight and the other is for the brake light. Hence the two dimples on the bottom of the bulb and the two dimples on the inside of the socket. Both dimples are the power or positive side of the circuit and the outer shell of the socket is the ground side of the circuit. Be sure you're using the correct 1157 bulb and that it's installed correctly in the socket. Hope that helps! Jim

I still have cars from the "60s as well, even the "50s. They're so simple. one light out indicates a bad bulb. If not, it's a corroded/dirty socket or a burned out wire to that socket.