Found 2 sources of peep sight movement on the Williams FP sight mounted on my Knight Bighorn. The first is that the peep insert had backed out quite a ways from the threaded hole it mounts in. In addition, I found that this entire peep housing, which slides on a threaded rod for Left-Right adjustment also has a bit of play and wobbles.
Resolving the first is simple - crank it down hard, maybe use thread lock, and check regularly. The second, I'm not quite sure.
Reaching out to others with this same sight to see if they have had similar experiences, how addressed, or maybe this just isn't substantial enough to worry about???