Hi Rob,
For enlisted haubes, I use a heavy 0.55 mm linen thread that I purchase on eBay from a leather supply shop in Alexandria N.Y. I use black or light tan dependent on what was originally used. I have seen original helmets with a mix of black and (originally) white thread. For officer helmets, I use a lighter gage black linen. I used to use upholstery grade thread, but it has synthetic fibers for strength, so , I now use the more traditional linen. I always wax the thread a couple times with bees wax. It keeps the thread from twisting as badly, and makes pushing the needle through the holes easier. Prior to stitching, ream the stitch holes using a small burr the size of your needle in a Dremel tool, otherwise you will have a near impossible time making stitches. Sewing pattern is to make an S pattern from one end of visor to the other end, and then return stitch to the beginning end alternating the pattern thus completing a figure 8 pattern. This way, there are no skips of thread between holes. You will need good lighting. Look back at other restoration forum threads that Brian and I have posted on sewing technique.
Ron