I think car badges became quite popular in the 30s. From the design and material, yours is obviously an early one. They are highly collectible and easily restorable...very nice relic!!
Great find. Would like to see what you can find out historically.
I found one from the same era (different design) that is for the Southern California Automobile Club, which I assume (cannot confirm) that it eventually became a part of AAA.
My guess is from the 1910 thru 1920 when the wealthier faction were members of the first touring clubs...now know as the auto club.
These were bolted to fenders and bumpers (or light bars).