Bad ground or bad switch
Even after replacing the switch it needs to be aligned with the shifter. Put the car in reverse and then have someone watch the lights as you loosen the switch and then rotate it slightly forward or backwards. once the lights come on, secure it in position.
I would guess the headlight dimmer switch on the floor board is bad or has a loose wire. Possibly the head light switch is bad. The headlight switch has a separate circuit breaker for just the head lights.
in glove box
How the brake lights work on a 66 Mustang is very simple. Power goes from the headlight switch to the brake light switch, then through the turn signal switch and back to the brake lights. There is no fuse in that system. There is a self resetting circuit breaker in the headlight switch, but, if that was tripped, none of the lights on the car would work. The first thing to check is the brake light switch itself by bypassing it. Unplug the connector from the switch and run a jumper from from one slot in the connector to the other. If the brake lights come on, replace the brake light switch. If they don't, the problem is either a wire has lost continuity or there is a problem in the turn signal switch.
Check the bulbs- they are double filamented with the smaller for brake lights Check the fuse Check the sockets for power and ground Check the sockets for corrosion
The Ford Mustang is and has always been one of Ford's most popular model cars. In 1966 the average cost of a moderately equipped Mustang was right around 2450.00.
Unscrew bezel and switch should slide out through the rear (under dash)
look on the side of the transmission.
ford mustang 1966
check your fuses and the brake light switch above the pedal
Check fuse Could be a bad switch