Looking for help finding a second hand

Need some help finding the proper second hand for this Ultra Chron. My watchmaker believes the current one is a replacement as the tip looks like it has been trimmed from a longer one. He believes it should measure 10.5 mm. Does anyone know how it should look like and where to find one? My ebay search was unsuccessful.

The hole size is 0.21mm, if you find a match for that and the length required you can order a generic part that will fit. Personally I think it's a futile exercise because the one on it already looks fine and presumably works.

I'd be interested to learn anything you know about this series of watches, I picked up an octagonal case watch with the same dial a few days ago. I've also seen these in square, rectangular, and squoval.

Not an Ultra-Chron, and it doesn't even have a seconds hand, but my example from the same collection is quite minty. Just arrived from the watchmaker today.