This whole "how does the bilge pump work" has always confused me. To make matters worse different years of boats seem to act differently, so the combination of most owners not fully understanding how it works and different year boats doing different things, you get a thousand different stories from everyone.
So far, from what I can tell, my 2017 212X has 3 modes on the connext control of the bilge pump:
1. OFF, the bilge indicator on the Connext is GRAY colored
2. ON, the bilge indicator on the Connext is GREEN colored - bilge is on continuously.
3. AUTO, the bilge indicator on the Connext is BLUE colored - bilge cycles every 3-5 min and sense if there is a higher amperage draw on the pump indicating that there is water being pumped, if so, continues to pump til the water is out - if not, turns back off and waits another 3-5 min.
Now, that I have said all this, to make things more confusing - it does not seem that it matters what mode the bilge Connext indicator is on when I shut down the boat completely but leave the house battery on - it appears that it is ALWAYS in AUTO mode in this case.
Am I 100% sure that the above is accurate? No, maybe 95% sure. Its what I've gleaned from others, the manual, and observation. But again this is the 2017 212X and it is pretty apparent to me following bilge threads on this forum that different boat models and years act differently.
Edit: Forgot to add, when both battery switches are off, the bilge pump does NOT operate.