Don't know if this is some type of tool or not since I don't know what it does. Got it with a bunch of farm wrenchs but don't know any connection. It does look old and I've never seen one;how about you ?
Supplemental info; Wooden cylinders are free to rotate; no markings; looks to be commercially made.
Broom handle clips you would wall mount. Press the broom handle between the rolls and they open on a spring. Thus holding your mop or broom upright in the closet or garage.
You are dead on strik9. My only excuse for not knowing this could be that brooms are outside my experience range.