So you know your converter is working properly so when plugged in to shore power, it's supplying enough amperage to operate the 12v water pump without issue.
However, without shore power, the battery 12v is supplying the source of power and that's not enough to keep it from flickering.
I agree with Lloyd that it sounds like a grounding issue off the battery or the connections before the pump if the batteries are in good shape. Expect to see 12.6-12.8 volts when testing them static.
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