I had one that was flopping around as described. It was the type of rear sight with a standing leaf flanked by a folding leaf behind and a folding leaf in front. The front leaf was loose.

I drifted the sight assembly out of the rib and found that each folding leaf had a small leaf spring bearing against the sight leaf. When upright, the leaf spring lodged in a flat on the bottom of the hinge part of the sight leaf, thus holding it upright. The little leaf spring for the front sight leaf was broken.

I fabricated a new leaf spring using a binder clip for material. I cut the leaf spring out using a cutoff wheel on a Dremel tool, then smoothed the edges with stones. It now works perfectly. Easy fix.

Curl