Since we are sharing methods here is how I did mine:
Cap was turned as normal.
The barrel blank was cut over length and drilled to the depth of the tube plus a bit to clear the end of the nib.
Tube glued in with epoxy. Used a tube inserter and wiped off the excess glue before removing it so no need for messing about with potatoes.
Once the glue was cured slid the blank ono a transfer punch that was a good fit with no slop and mounted it in a keyless chuck in the headstock.
Supported the tailstock end with a ring centre with an adjustable centre point and turned the main body of the barrel to shape.
Sanded and polished the main barrel. Rhyogrip/micromesh/Farecla
Swapped the ring centre for a 60º centre to allow access with a small gouge to shape the end.
Parted off the end with a skew.
Removed from lathe, end sanded with Rhyogrip and polished by hand with micromesh then final buffing on a buffing wheel with white diamond compound.
I will be writing an article for Woodturning later in the year covering various tools and methods for making closed end pens. I will mention any tips that I have seen here that I think people might find useful.
Once my articles have been published I will make them available on my website. The first one on CA finishes will be in the February issue (No277)
