I've been working in a workshop where we repair double basses for over ten years now, if there's a broken headstock, we use epoxy based glue to repair it, it's strong, durable, filling and it dries quickly. We NEVER use hideglue for a repair like that, hide glue mostly is used to repair cracks and splits in the top, bottom or sides of the instruments. If we have to glue in a neck we either use the epoxy based glue I just mentioned or Titebond.
As for our guitar building, we always use syntethic glues like the epoxy stuff and Titebond because they are dependable and strong.
"The name is bond, titebond."