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NOTE: It's 6V, so it won't run off a PF pack. Not sure if there's such a thing as a waterproof four AA or AAA pack with switch. You would also need small waterproof wire connectors. And no, no pumps seem to ever include a battery pack unless they're part of some educational kit.
I have a couple of these that are connected to an Arduino to water some plants. They are submersible, small and battery operated. But they are more of a dribble than a jet. Cost me just under a quid each on aliexpress.