What did Mr. Parker; Bud's & Mary Sue's father do for a living?
There was an an scant mention of perhaps a promotion at the first of the movie. And later, the Mayor drops by and invites him to the Chamber of Commerce....but wouldn't that "honor" go to the business owner and not am employee?
Okay, watching a 3rd time....
You always have to keep it firmly in mind that they weren't real people in a real town, just characters in a 1950s B&W family sitcom. So if it wasn't in the script then it was absent information. It is likely that the character himself didn't know what his job was if none of the episodes had him at work.
If you watch some of the family sitcoms of the 1950s and 1960s it was normal to see family men going to work without explaining exactly what they did. In this movie it never was important to know what his job was, only that he was the sole bread winner, he had a routine, and he came home wanting to know what was for dinner. His character was a parody of an ideal husband in the 1950s.
Regarding the Chamber of Commerce, those are small organizations that lobby for the businesses in the area and settle small business disputes if there are any. Of course there would not be any disputes in B&W Pleasantville. While the usual membership are business owners it would not be unusual for a trusted employee to be a member in lieu of the actual owner.
But in this movie it is just used as a symbol that he is being recognized, it would not help understand the message of the movie to try to analyze his job in too much detail.
..*.. TxMike ..*..
Take a risk, Take a chance, Make a change. Kelly Clarkson - Breakaway