I have two gray tanks and am now thinking about putting dye in one filling it up and seeing if I get dye out of the other valve.
I have often thought where did I get so much water when dumping that back tank. I have an out door kitchen that I know drains to it but I often have a lot of water in it that I have no idea where it could have come from as I do not use that sink very often and then never run a lot of water. I suspect they are connected.
I have never had the grey or black water be a problem even after camping 7 days without a hookup that was with 3 people.