Welcome!!!
It is not likely to be an overflow in the normal sense. Those trailers/motor homes with a second grey tank usually have it connected to the bathroom sink, the shower or both. The first tank is usually connected to the kitchen alone in these cases. Some may have the bathroom sink connected to the black tank when a second grey has not been provided.
Hopefully you found a shut of valve for that second tank and have not left it open so it drains all the time. Nothing wrong with that if you are aware of it and hooked up but.... it's best to know. BTW, NEVER run with the black tank open all the time, hooked up or not or you will likely create problems you would rather not have!!! (Look up poop pyramids).