Ok the issue with 3 lights MIGHT be the generator.. here is why
There is an electronic component called a capacitor the symbol is -||- (note the dashes actually connect to the verticals) this is symbolic of the construction. Two metal plates with an insulator between them (Even air)
Well you have hundreds of feet of ROMEX cable and for this purpose that can be drawn as -|||- with the safety ground sandwiched between the hot and neutral
or more precisely -||--||=
Now in a DC system. that don't matter
But in an ac SYSTEM that forms what is called a voltage divider
So with reference to the NEUTRAL the HOT lead is 120VAC-RMS
And the safety ground 60 VAC-RMS
On many generators the Safety ground is NOT bonded.
And there is your 3rd light.
IS this dangerous? NO, not at all
Why the safety ground
House/Shore power IS bonded and in multiple places (The pole. your entrance service box) and heaven forbid you pick up a hand grinder like one I used for a bit professionally with an internal hot to case short .. YOU become a "neutral" path.
But the generator is NOT grounded so that does not happen.
