Yep, the ground wire is attached to the bushing that the tailpiece post screws into.
If you want to pull it out:
1. Use a very thin blade to cut around the edge of the bushing so the finish does not chip when pulling up the bushing.
2. Make your own "puller" tool using a long bolt that fits the bushing
3. Use the tail piece post or long bolt and a claw hammer (!
)
Obviously you use some rags and pieces of wood on the top of the LP for the force of the puller or hammer to press onto.
Personally, I would have to get a luthier to do it...
It's not the greatest system in the world having the bare wire pinned against wood and bushing, and yours has lasted 30 years so that's not bad! There's a guy who came up with the idea of using a spring that sits in the threaded hole in the bushing with the ground wire soldered onto the bottom of the spring. That way when the post is screwed into the bushing for the tailpiece it is always pressing hard on the spring.
http://eksomething.blogspot.com/2009/02/les-paul-build-part-8.html
To do this you would still have to lift the bushing a couple of mm just to get the ground wire under it, unless the bushing doesn't go all the way down the full depth of the hole in the body. If this is the case you should be able to run another piece of wire into the bottom of the hole and hook it up into the threads of the bushing where the post will hold it in place, which would keep you going for a while.
Why did it come off? Maybe just corroded away, or the pot has been turning in the past and put some strain on it or something.