Did he have a job? Was it ever specified?

I think he was some kind of lawyer...I think it was in estates (big surprise, huh? :lol:).

I thought he made a living dabbling in the stock market.

He was a "professional" stock trader, I guess. He "worked" at home. I'm not sure if he ever had an actual job though. Who'd hire him? :lol:

But he also dabbled in real estate from time to time.

I always thought that since the Addams family lived in a big mansion (a big weird scary mansion) that Gomez was independently wealthy.

An eccentric millionaire if you will.

According to Jack Sharkey's 1965 novelization: Gomez had his own "beloved
tickertape machine. (He'd first purchased it, many decades back, when its
name made him think it was a sort of specialized gadget used in open-heart
surgery; by the time he realized he'd been misled by his pun-loving mind, he
had grown interested in the stock market; and once he learned how often one
could make a killing in the market--legally, too!--he became a professional plunger and made millions.)"