Some, used to use old gramaphone needles. A common thread for the needle if made in 1 piece, like the Super Tigre or Rossi needles, uses the M2.5 thread. I think is 0.4mm pitch.
The needle insert, or pin can be made from 1mm piano wire or wire size slightly larger than the inlet hole. Then I use a piece of balsa wood as a support block, and use a Dremel to grind the taper on the pin. Anywhere from 5-7 deg per side works really well. I use 5deg mostly. For a Ø1.2 mm needle, it is about 6mm long the taper.
A small collet chuck like an ER11 makes them easier to make.
On my F2A NVA assemblies, they do not close to zero. That way, the needle taper can not be damaged by the edge of the inlet hole in any way. Damage to the taper seat or to the needle can make it inconsistent for its repositioning.
Neil