Jim: I have turned them (got the kits from Craft Supplies). There is a pic of one in my album. You can see that the pen is tapered too! The tube is 1/4" outside diameter.
Best way to drill for this kit is right on the lathe. Also helps to have both a 6" long and a short drill bit. The reason is that longer drill bits can flex some. You need a drill chuck with a Morse taper for the tailstock, and it helps to have a scroll chuck too.
Unlike other kits, I like to start with a 1/2" or so round dowel, about 9" long. Chuck it with as much of the dowel as possible going into the Morse hole in the spindle. This steadies the dowel. I like to make a pilot hole with a smaller drill first. Start drilling with the short 1/4" drill bit, and end with the longer one. Reverse the dowel, and drill a very small and shallow hole for a live center.
I did not use the special mandrel. A stick of hardwood turned down to fit works fine as a mandrel. I chucked mine in the drill chuck in the headstock, and used a live center at the tail end.
The finished pen will be a little shorter than the dowel, because there will be a little waste at the tailstock end. After turning and sanding the body, I work on the tail end until there is very little wood holding it to the waste. I can part it right on the lathe at slow speed, holding the pen near the end with my hand, it acts like a steady rest. Otherwise you can cut it off by hand.
Cup centers work well with this type of spindle work. I make mine out of wood, and put a piece of soft material between the pen and the cup if already sanded. I have a live center with replaceable points, one of which is a small cup center, but wood will do well too. You can contact me if you need tips on how to make one.
By the way, the tip screws into the tube. This is the only way to change the refill !!!