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In addition to Joe's advice, I think it wise that you attempt to trace the wires from the bilge to the battery. I would also look at the back of the bilge switch on the console.
As you know and the owners manual states, be warned that if the bilge is directly wired to the battery, it can run the battery down to the point where starting the engine is not possible.
If you have a Mercury Optimax motor, I have read they demand a well charged battery to start.
Once you sort this question out, and determine the water level with the plug out, you may want to consider adding a second battery for the bilge. At this time, I recommend you do the investigations suggested above before you consider a second battery.