The reverse polarity light checks for a difference in potential between what should be the neutral and ground. The neutral and ground from the shorepower are not connected on the boat but are back at the pedestal on the dock. If the connections between the hot and the neutral were reversed, the light would see the difference between the hot and the ground and be illuminated. When you have another source for AC power right on the boat, such as an inverter or charger, the neutral and the safety ground at the output of the device should be connected. I don't know what kind of inverter you have, some take care of this connection with their auto transfer switching. If you don't have the neutral and ground connected you probably have a potential large enough to illuminate the reverse polarity indicator lamp
