Not sure if this will help, but I will offer what I have researched on these cateye reflectors. The older (late 1920s ~ patent pending) libbey reflectors are very hard to come by like the one you have, I have only been able to find some green ones, and been shopping for these constantly over 3 years.
In the 1930s manufacturers went different sizes and style than the one you have pictured...and somewhat standardized their sizes. The most common manufacturers are Libbey, National Colortype, Persons, and Signal. All four of those manufactures used a number system of 1-5 (National Colortype used 11-(followed by a digit) to 15-1) to indicate the sizes. I know Libbeys, Signals, and National Color Types will all be marked on the back.
I hope my sizing chart uploads for reference. These are later style libbeys which would be held in place with a mounting cap on the back side. Smallest is a Libbey #5 (17/32), Largest is a Libbey #1. I believe you could make a #2 work the flange appears wide enough to hold. The #1 will not fit a 7/8's mounting hole.
Looking for National Old Trails Road Signs NOTR and Arizona State/US Route and Road Signs.