My customer has a problem with his handmade archtop. A tailgut is holding the the tailpiece and there's no room for a strap. This was a job for a new addition to the shop, the Taig lathe. Make an endpin with two grooves in it, one for the tailgut and one for a strap.
It was straight ahead, ish, the taper on the end pin had to match the taper in the end block. A small tapered reamer was used to clean out the existing hole and provide a reference point. The outer most part of the reamer was marked and measured. Calipers were used to transfer the largest and smallest parts of the taper. After shaping, the peice was cut from the blank and final shaping and polishing were done in the drill press chuck.