I’m delighted you like this project so much that you’re planning to make a convertible beaded necklace/eyeglass leash yourself. When the strand is worn as a necklace, the two clasps attach to either side of the jump ring. So, I assume your question is how to avoid losing the jump ring when you want to convert the beaded strand from an eyeglasses leash to a necklace.
One option is to place the jump ring (preferably in a very small zip-top plastic bag, roughly 1.5”) in your jewelry box or jewelry drawer until you’re ready to convert the eyeglass chain back into a necklace. Another option (the one I usually use) is to detach only one of the clasps from the jump ring, so it remains attached to the other clasp when you’re attaching the eyeglass holder end to that end of the strand. Since the holder end findings attach to the glasses’ “arms” just in front of where they start to curve down around the ears, I find that the small, hanging jump ring isn’t very noticeable.