I wouldn't use Gorilla Glue for fine woodwork! Certainly not for luthier work!

My brother used to make fishing nets (I have one) using hide glue. You can still get this, but you really have to search it out. When I was making tombstones the freeze/thaw cycle would sometime make letters "pop". "A", "B", "P" and other "closed" letters were particularily susceptible and the center of the letter would break free (the triangle in the "A", for instance). The families would come to The Boss, who had made the stone, and ask that it be fixed. We could and would do so, especially if the broken piece was available, as it usually was.

We'd clean it, epoxy it back in, and charge 'em $50 -- most of the cost was simply the cost of taking the truck, etc. out the cemetery. If the cemetery was close by (like the one across the street) and the stone was pretty recent we might not charge them at all.

I've noticed that there is a line of superglues being marketed for various types of plastics now.