The reason for the ground solenoids on both the Onan and the main motor is to isolate the battery negative from the ground which connects all the seawater connected metal parts, which are connected to your anodes on the rudder.
Without this isolation, there is the possibility of stray currents running from the ground to the electrical system which can cause corrosion inside your engine, genset etc.
You should have a ground solenoid in your engine starting circuit.
