Hi Leo,

That button is called a pin back.
I got it last weekend at the NSRA Western Street Rod Nationals in Bakersfield, Ca.
1800 Hot Rods. I drove my 1930 Ford Model A.
They give the pin to all the entrants, it gets them in and out of the fairgrounds all weekend.
I have a bunch from different Hot Rod shows that I have attended.

Best,
Ralph