I'd use a drop of yellow carpenters' glue like Titebond.
-1962 Martin D-21 -1950 Gibson LG1 -1958 Goya M-26 -1974 Yamaha FG75 high strung -A number of banjos, mandolins, Autoharps, ukuleles, dulcimers, mouth harps, a Tele clone and various other stuff. -I own a fiddle, but only play it when Maggie and the cats are all out of the house.
@sleigh, there's really no reason why you would have this, I do woodworking and I don't have any, but if you really want to glue it hide glue is your best bet. It was used in instrument making up until the modern age. It's strong and it has the advantage of being easily unglued with a little warm water. Maybe if you know someone who's really into traditional woodworking...?
Just 2 small drops of white wood glue using a tooth pick is all needed or hide glue. Most are glued in place, just takes a tap with a small hammer and block of wood to remove one and a bit of work to get the glue off. Some factories add far to much then the risk of wood coming off exists, it's fixable . I just use 2 small drops with a tooth pick and they come off clean and stay there. Sometimes if you use no glue and tune up with new strings the nut will tilt which you don't want. Strings pull at the top and the nut leans. Depends some guitars the nut sits between the finger board and a head stock veneer which is a sort of shallow slot then it needs glue just to keep it there no strings or no glue at all if it fits snug enough.