My FIL had alot of stuff like this. He told us at one point that these were old headlights. I thought they were miner head lamps. The only one I found similar was on ebay as a miner light, but the strap to fit onto the hat is different.
The ones we have, the strap in the back look like they are a hand-held light.
The only oil headlights I could find seemed to be for mostly trains, but I did find something similar, yet different for a ford model T.
I'd like to find out for sure what these are, and a date for them!