I do not see any way to attach it other than the 4 holes in the back plate, …. which implies the back plate was removed for installation and re-affixed to hold the mechanism in place.
It appears the handle can only be moved less than half a turn (it can’t be turned full circle) …….. and it is aligned with the projection (arm) on the shaft which may or may not be significant.
Given said, I have decided it could be or probably is .... a door-bell or a servant-bell because in the old days, there were all sorts of things that were used to "call a maid or butler" or to make one's presence at the front/back door known and such a mechanism would work just fine for doing said.
With a "ding-a-ling" bell in the kitchen, maid's quarters, etc., .... attached via a wire or cord to the "arm" of your mechanism, then a slight movement of the handle would ... ding-a-ling-a-ling-a-ling that bell where ever it was.
cheers