I don't know what kind of finish for sure but you can test it with lacquer thinner to see if it etches the finish at all. Check it inside a pick up or control cavity. If it softens the finish it is lacquer if not its some sort of urethane or two part whatever.
I did a neck repair on a PRS which are finished with a two part urethane. All I had on hand was some gloss cabinet grade urethane so with a foam brush I applied about three good coats. Let it cure for a week, sanded and buffed as normal and it looked sweet. Couldn't see any cold joint kind of shadows and it glossed up like the rest of the neck.
If it turns out to be lacquer I would spray and than cure, sand ,buff as normal.