That light contains a diode that illuminates if the neutral wire has a higher voltage than the ground wire. Which is designed to detect a full 120V fed into the neutral instead of hot but can also illuminate on just a few volts of imbalance between the ground and neutral.
The solution would be to bond the ground and neutral at the generator. This is similar to a house in which all the ground paths are kept separate from the neutrals until the point that the buildings electrical system is grounded.
Here is an article that may be useful for you;
https://www.rvtravel.com/rv-electric...onding-basics/
I made one of these and plugged it into the other generator outlet. I also used a GFCI on the shore power cord at the generator. Probably overkill but I figured it was good practice to be sure that every amp which left the generator came back to the source instead of going somewhere else (ie the water).
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