Yep, my trailer doesn't have a light on the plate either.
Came that way from factory.
Never had an issue with the cops over it.
I need to move mine as it's getting beat up and could easily suffer the same fate as the OP's.
My first boat I used a flat bed trailer to haul it around.
It was hard to see the plate so I hung it on a chain around the OB so the cops could see it.
Got pulled over and they said it needs to be on the trailer and that it didn't matter if they couldn't see it.