Here's how I complete (pull through) winding wraps. It seems so simple and obvious that I'm surprised that this little technique isn't universal: Just make several loops of light (say, 3X-6X, or 3-6 lb.) monofilament, or rod-winding thread.
Cut off a 6-7-inch length; tie the two ends together. You now have several little ovals. Tie an inch or so of bright yarn to them at the knot, so that you can easily find them on your bench. Make several, because they do eventually break at the apex.
Normally, six wraps over the mono loop seems to produce optimum tension. I usually cut off the thread close after pulling it through, but here's how to do it more neatly, hiding the thread end: Put the thread end into the mono loop and pull it against the end of the winding, tight enough to hold the thread for a moment. Then cut the loose thread end about 1/16" to 1/8" from the mono loop; pull the mono loop through.