I feel kinda dumb asking this, but I'm not familiar with some of the details of the '77s, one of which I now own.
Last night, after driving the car, I was walking around the back of it and I noticed a light coming from underneath. Kind of between the spare tire carrier and bumper. It went out after a few seconds, so I'm thinking that I have a courtesy lamp of some kind.
Today I go to remove a trailer hitch that the previous owner had installed, and I notice what I thought was the courtesy light just hanging by its wire. I remove the hitch, then take off the license plate light, identical to the courtesy light, in order to remove some overspray from a prior paint job. So both lights are now just hanging there. One inside the body work, the other out. I turn on the lights to test them, and only one works - the license plate light. I turn the lights off thinking that this courtesy light will work for five or ten seconds, but it's a no go. I replace the bulb just for grins, and still nothing.
Am I losing my mind? Do these cars in fact have a courtesy light, and if so, what does it screw to?
Ok, easy stuff out of the way.
A courtesy light would be in the interior, don't think this will reach based on your description. Is this a add on or does it appear factory? You need to look at a wiring diagram, if it appears factory. I guess it is not a side light , couldn't reach again.
Does the socket have two or one wire to it? Do you have all sockets accounted for in the rear lights? brakes, tail, backup.
You could try grounding it to see if it will come on.
I have a 77 but only have the license plate light and regular tail light bulbs -- no "courtesy" light for the spare. As recommended above, make sure you have all the bulbs into the tail and side lights. If so, then someone must have added the light because I do not know of any "courtesy" spare lights on a 77. Maybe it was something to do with the trailer hitch.
Tom73 had it right, on my '79 the license plate light is wired to the headlight switch. The courtesy light is triggered along with the interior lights (door open). This is designed to give you some light when you're working on getting the spare lowered on the side of the road.
Since it is in the same circuit as the interior lights, the delay module also illuminates this light for a while after you've shut the doors.
All the side and tail lights are accounted for. As well as the license plate light. The courtesy light I'm referring to is identical to the license plate light. It doesn't ground to the body, so it has two wires going to it, and it comes off of same wire harness that has the license plate light (as well as most of the others).
I don't see where it screwes to on the frame work. It's on a short pigtail, no more than about 8" long. So it's got to mount somewhere very near the spare. I'm thinking that it was taken loose and left hanging there when the hitch was mounted. Maybe there was some kind of conflict there.