The back up light switch is mounted directly to the transmission. When you engage the shifter into reverse, the shifter physically actuates the switch's button, turning the back up lights on. It's a simple, but effective little system.
Note: If you're doing a T5 swap or a similar project, the original back up light switch bracket will not adapt to the new transmission. You will need to have one custom fabricated.
there is no fuse for the reverse lights check the netural safety switch it may be out of adjustment or shorted.
how to replace the netural saftey switch
check the netural safety switch on the transmission valve body. only if auto trans
The multifunction switch inside the steering column is bad.
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.
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.
If fuse is ok, could be a bad headlight switch
On a 1993 Ford Mustang : Open the trunk lid or the hatch Between the rear tail lights you will see an oval shaped rubber plug The inertia switch is behind the rubber plug
On a 1989 Ford Mustang : The fuel pump shut off switch ( inertia switch ) is in the trunk / cargo area It is between the tail lights and is covered by an oval shaped rubber " plug "
The switch is wearing out on the inside, just order a new one and replace it.
its in the steering column its in the steering column