Well, the light is energized by the control board on the generator. I have the manuals for my 1999 5500 Marquis and it shows the light between pins 1 and 6 of the remote connector (P2 on the control board). If you unplug that connector, the light should go out. You can then measure voltage between the 2 pins. There should be none if the generator is not running. If there is voltage, that would seem to indicate that the control board is bad.
That is not an inexpensive part. If the generator is functioning properly, I am not certain that I would spend the money to replace that control board just to turn the light off. If you are into electronic work, you can get the service manual for your model generator and it includes schematics for the control board.
1999 Newmar MACA 3796 F53 6.8L
2016 Ford Edge Sport
Roadmaster Sterling A/T with Brake Buddy Select