It's a movie cliche I know we've seen several times, where the outsider discovers (with hilarity) that the town mayor is also the town ______.

Having watched Cars for the millionth time with my boys, the first one I can think of is Paul Newman as Radiator Springs' judge, mayor, and mechanic. What are other examples where this happens?

Any movie with Judge Roy Bean might count. Paul Newman, coincidentally, played him in THE LIFE AND TIMES OF JUDGE ROY BEAN (1972). Walter Brennan played him (and won the Best Supporting Actor Oscar) in THE WESTERNER (1940). Victor Jory played him in Audie Murphy's last movie, A TIME FOR DYING (1969).

I don't think Doc Hudson was ever described as mayor. According to wiki, he was judge and physician.

Interesting... I wonder if I jumped to that conclusion since he's the vocal leader of the town.

In Do the Right Thing the mayor was also a homeless drunk.

Roxanne: the mayor (played by Fred Willard) also worked for the fire station if I'm not mistaken.

In National Lampoon's Vacation, Clark asks the mechanic who's ripping him off, "What does the Sheriff think of your business practice?" The mechanic replies by showing Clark his badge.

Edit: Just realized that didn't answer the OP's specific scenario, but it's close.

However, John Mayer performs on the soundtrack, so there you go.

In probably 95% of towns in the U.S., the mayor actually does hold a day job.

Mystery, Alaska and Doc Hollywood maybe?

High Plains Drifter

The rectum-mangling Groucho received from Cars can never be fully documented...

Kinda-sorta:

The Reverend Clayton is both a minister and a Texas Ranger in The Searchers.

Wasn't this the case in Nothing but Trouble?