Don't really buy the term "invisible". An umpire should just work the game, use the prescribed mechanics and signals. Do not ad lib calls and rulings to place oneself in before the game.
It's not so much being "invisible", but working at a level in which you are no more noticeable than other equipment used during the game.
Of course, there are always the moments when teams don't give you much of a choice than to make yourself known
