Taken literally, 3-3-1j would say that players can't go to (as opposed to already being in) the bullpen, there can't be a batboy, players can't chase foul balls, etc.
The casebook heading for 3-3-1 is "Leaving the dugout/bench during a live ball", and it says the intent of the rule (presumably 3-3-1a) is to limit offensive players from flooding the plate area. I'm dubious that 3-3-1j applies between innings or during an in-inning pitcher change.
Even during live balls, other folks besides those mentioned in 3-3-1j are authorized to be outside the dugout. For example, it specifically says that the batboy is OK, and that players can go down the foul line to the bullpen.
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