Back in the 1920-1930's automobile travel for fun, really became popular. There were a number of automobile clubs that you could join that offered giving you access to trusted service people across the country during your travels. They also published maps and vacation guides etc. BTW, look online or local bookshop/antique stores for old copies of these guides they have lots of ads from bygone attractions, funspots, picnic areas, resorts etc.
This does look like an emblem that you would have mounted to your car, to prove membership.
Hard to say about the curve to it , except that cars + bumpers were MUCH curvier in the 40' & 50's than they are today. Might also have been mounted on a pole at participating service center AKA local garage.