Found it in my late father's tool box.

Anyone know what this would have been used for originally or if I have all or some of it?

Looks like a vintage hat hook with a missing "round" piece to not damage the (cowboy) hat? Usually they are a combination hat and coat hook but that one looks more like just a hat or you put the coat over a ball piece and the hat on top of the coat?? look up horseshoe coat and hat hook and see what you think.

Has to be mounted the way your photo is (open horseshoe end up) or all of the good luck runs out mounted the other direction

Thanks A12! A missing ball would fit.

Wonder if a painted or a colored miniature (putt-putt ) or even white golf ball would fit?

A "Super Ball" from the local "dollar" store might work also ?

Yeah good ideas. I originally thought it was for a candle holder and you stuck something up through the hole to hold the candle in place, but the melted wax would go everywhere.