The correct rear reflector for the ‘63 and ‘64 J38 Standard is the Stimsonite (2 pie) that measures 1-3/4’’.
My Red ‘63 and Lime ‘63 are shown below with their small 2 pie.
The larger Stimsonite (2 pie) at 3-1/4’’ would have come on the Deluxe models in ‘63-‘64.
Starting in 1965, all Standard and Deluxe models came with the Large reflector.
The Stratolite (6 pie) would be on the later Stingrays / Krates.