Might've been for a tommy bar to snug it up once it's hand tightened. Same idea as a vice or c clamp with it's sliding handle. Wouldn't stick out at an odd angle in the way with it being removable too.
I have a lamp with a similar holder, but I'm not going out in the rain this evening to go and get it.. I think this is a clamp on holder for something.Not a tire vulcanizer. I had an articulated lamp with a holder like this. The lamp had a stud that inserted into this holder.