Actually, yes, we did have some stage plugs, but it's not the right size for anything related to that.
As to a stamper... You mean a rubber stamper? It seems a bit hefty for that, and if a metal die stamper, it's only hand-held with no indication that it was struck with a mallet. The recession is also over an inch deep which seems overkill for a stamp insert. But so far, that seems the most likely suggestion, though why it was in the dimmer room is also a mystery.
Maybe it was before they had the automatic stamping devices where you pulled the guys out and adjusted the stamp then slapped it back in. But like you said why it's in there is beyond me.
It is inserted over the end of very large breaker switches, usually the master breaker on large lighting panels. It gives a mechanical advantage to turn the breaker on or off more easily. I have encountered several of them and been thankful for them. This was for panels that were installed from the early 70s to the late 80s.