I questioned some of the old timers (70+years) that I surf with and they recall hearing the expression used in the mid 40's to refer to anyone who was acting like a jerk, not just a youth. A retired navy captain recalls hearing it used during WWII, in the same manner, i.e. as an euhemism for asshole.
It makes sense that it would originate with the navy, as a 'grommet' is:
Another interesting piece of slang that was on the beach in the 40's was beasel, beach+weasel, meaning a beach thief.
Ron St.John