FWIW, another suggestion: Forget turning that part as it is not easy to turn something so thin. I would just make the "button" part using a piece of drill rod. Drill out the center on the lathe, then cut to the right length. Then insert a piece of small rod (drill rod or Brownells spring wire stock) of the right diameter into the button and silver solder it in place. That way you can easily make one with as much length as you need, then cut to the correct length.