Re: Connection between Dome Light and Radio
It sounds like whoever did the stereo installation tapped into a part of the harness/fuse that the dome light is on, and when the lights come on, there isn't enough juice left to run the stereo.
It could even be that the orange wire for the lights was tapped for the 12V power feed to radio.
The way the dome light/courtesy light switch circuit operates is that the orange wire to the bulb sockets is a constant 12V hot wire. The white wire from each socket goes to the jamb plunger switches, which are normally open when the doors are closed. When the doors are opened, the jamb switch grounds to the body and current flows allowing the lights to glow. There is a separate white ground wire in the system that ground the circuit to the dash ground when the headlight switch is rotated to turn on the interior light(s).
An easy check would be to remove the bulb(s) and see if the radio still shuts off. If the bulb isn't there, the circuit is not completed through the socket, so the 12V hot would stay available for the radio. Also, you can turn the headlight switch to turn on the interior light(s) (with the bulb(s) in this time) and see if that kills the stereo as well.
Either way, it sounds like you're going to have to undo the radio mounting (take off the battery ground; if someone used a random orange wire as a radio power lead, who knows what else is back there and you don't want to create any fireworks behind the dash) and hope hope HOPE that whoever did the install left enough wire that you can pull the stereo out under the dash and lay it flat on the tunnel. If you have a console, you're going to want to pull it out too, unless you've got skinny arms, are very short, and can read/view things upside down and back under the dash.
Depending on your size, you may want to start that way; in a really awkward upside down position with your head on the floor and/or jammed into the brake pedal, trying to look up behind the dash to see what kind of mess you may have to deal with.
If you can easily see the power wire for the stereo and confirm it was just tapped into an existing orange wire, the short term fix would be to remove it from the orange wire and just run a new 12V wire to the "ACC" terminal on the fuse box.
The correct thing to do would be to look at the AIM wiring diagrams (UPC 12 is electrical) and find the original radio power wire (for a 67 it should be a black with yellow stripe coming out of the main dash harness near where the radio mounts) and use that.
69 'vert project big block/TKO 600 RR
68 'vert driver RS clone -- gone!