To replace the headlight switch in a 66 mustang, you first have to remove the instrument cluster housing. After you have that out of the way, you will see a small button on the housing of the switch mechanism itself. Pull the switch knob all the way out, as if turning on the headlights, then push that little button and the switch stalk will pull all the way out of the switch housing. Then unscrew the switch bezel, pull the switch housing back, so that it clears the dash, unplug that big wire connector from the side of the switch, and remove the switch entirely. To install the new switch, you just do what you just did, except do it backwards.
Unscrew bezel and switch should slide out through the rear (under dash)
Bad ground or bad switch
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.
Floorboard
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.
Change the headlight switch. If the switch fails to fix the problem, you may want to pull the headlamps out and check the connection at the back. Lastly, inspect the complete headlight wiring harness for missing insulation, exposed or frayed wires, or loose firewall connection.
in glove box
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It unscrews.
The headlight switch may be at fault or the wiring has been altered.
The 1966 Chevy Impala ignition switch can be removed by loosening the retaining ring at the top of the ignition switch. Remove the wiring harness. Reverse the process to install the new ignition switch.
ford mustang 1966