You have a problem somewhere, that's for sure. First off, you say the taillights are dimmer than usual, but then say when you turn on the headlights, the taillights don't come on at all. I'm guessing that you meant the brake lights are dimmer, since the only time your taillights should come one is when the headlights are on. So I'm guessing your tailights never come on at all. Do your dash lights work? Most all cars have the dash (guage lights) lights and taillights on the same circuit so you know from inside the car if the taillights are working or not. If you have neither taillights nor dash lights, check the fuse, if it's blown, you likely have a short somewhere in the taillight wiring loom. It's a very short, very simply circuit with few wires, so start looking for physical damage, like a bare wire rubbing on metal or a broken wire. If you don't spot something obvious, it's time to break out the multi-meter and start checking the continuity of wires. If you don't know how to use a multi-meter, now is a great time to learn, they are great tools for chasing down electric gremlins in vintage Mustangs, and they are very cheap.
