From your manual.
A little circuitous… I put the pages in the order that I think they should be in.
Page 122-Overview of Bilge pump operation. I will add, to the best of my understanding, when the bilge pump is in automatic the bilge pump in your boat turns on once every 2 minutes for 30 seconds to sense whether water is present or not then shuts off if no water is sensed. If water is sensed it will stay on until it has removed the majority of the water.
So to answer your question, it appears that if the connext screen is off after putting the pump in automatic the pump will run automatically.
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Turning the Bilge pump to Automatic from the connext screen.
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Turning the Bilge on manually from the connext screen
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Turning the Bilge pump on manually from the rocker switch.
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Test these operation modes of the bilge pump in the driveway to make sure they work as the manual states by installing the drain plugs and filling the bilge with water from a hose. Also, take the boat out on the water a few times and take note of either how many times the bilge pump comes on during the day, and or, how much water comes out of the drain plugs at the end of the day. I would say if you are going to leave the boat wet slipped, and the bilge pump comes on automatically during a day on the water you have a leak that needs to be fixed before leaving it wet slipped. IMHO the bilge pump should only be removing rain water that accumulates while wet slipped.
Questions.
1-How long are you planning on leaving it wet slipped?
2-Is there power available at your slip?