To MAKE a closed-end mandrel is really easy if you have a collet chuck that will hold 5/8" bar stock/dowel.
I use metal, like brass or aluminum. Some use wood, nothing wrong with that.
Chuck the material in the collet chuck, and turn down a tenon that is about 1.5-2" long and will make a snug fit for your tube. Use sandpaper as you get closer to the right size (sander belts are very, very tough and work great, I use 100 grit since I have a few damaged ones that I can scrap off).
IF PERCHANCE you get it too thin, never fear, for CA glue is here! Literally wipe on a few coats of CA finish (lol, don't micromesh it) to make it fatter for a more snug fit. Hose it with accelerator just to make sure it doesn't become a permanent part of your pen when you slide the blank onto it. You'll get a feel for what's right very quickly.
Don't worry about turning a bushing on it-- use your digital calipers to get the nib end right.
BTW, do ALL of your turning with the tailstock and live center engaged. Don't use a lot of tailstock force or you'll dimple your pen, but use the tail to keep it safe. When you are done shaping your pen, gently sheer scrape the butt end to the shape you want and remove any dimple. Sand, finish, and done. Piece of cake.
I love closed end pens. Simply sweet.