I am not an electrician. I have been waiting for someone else to weigh in but I’ll take a shot. The Honda 2000, like similar portable generators, has a floating neutral (really no neutral, but one side is connected to the neutral on your boat so we then refer to it as the “neutral” wire). It is floating because it is not connected to ground at the source. The neutral should ideally be bonded to the ground at the source *and nowhere else*. In a home, it is at the service entrance only. On a boat, it is at the shore power source on shore and not on the boat.
The one exception to that is when the inverter is the power source. Many inverters on older boats are wired incorrectly and create ground faults when the boat is connected to shore power. The owners often only find this out when they connect to a marina power pedestal that has been updated to the newest standards.
This brings us to the Honda 2000. When the Honda is plugged into the shore power receptacle on your boat it becomes the power source. Therefore it is ok and probably a good idea to ground the neutral at the generator. You can buy a special plug for this purpose that already has the neutral and ground connected internally. Then you simply plug it into the unused receptacle on your generator. (Never leave this plug in place, though, if you ever connect the generator’s output to your house wiring. The possibility that people may use their generators in that way is why the neutral and ground were left unbonded in the first place.)
If you bond the neutral to ground at the generator, it becomes functionally the same as when your inverter supplies power, and I think your meter will read correctly at 120VAC. But then there is the question of why it reads 60VAC now. Not sure, but I’m going to hazard a guess that your meter is connected between the hot wire and ground rather than hot and neutral. The ground on your boat will be connected to the metal frame of the generator through your “shore power” cord’s green ground wire. You are probably measuring stray capacitive micro-currents from within the generator since the neutral has been left ungrounded.
Anyone can feel free to chime in here but that’s my take.
Here is the link to the plug:
https://www.amazon.com/Southwire-Compan ... B07F4R7BDL
John