It was a
drinking game to keep people from driving drunk. I first heard the term in the late 1960’s.
Imagine a group of men in a bar, getting
inebriated and passing gas. When a guy passed gas, the men would have to state the name of their favorite beer, followed by 3 quick knocks. The one with the slowest response time was labeled the (slowest)
fart knocker; and accordingly had to stick around (as in not leave yet), as that was the most impaired person.