Hi Sharon,
Original rims had a rivet on top that secured a flat tab inside to mate with a slot in the top of the headlight rear mounting ring. This holds the rim securely at the top. There is a hole in the bottom of the rim for a sheetmetal screw that goes into a retaining clip. Your rivet has likely gotten it's chrome or nickel polished off over the years.
Most replacement rims just have a raised bump at the top with no internal tab. They rely on the turned down portion of the rim to catch on the rear mounting ring edge. Really, kind of an inferior substitute but much easier & cheaper to find.
D