Pick up a clear section of dump tubing such as
THIS. Next time you dump, once the tanks are empty close the gray valve and leave the black open. Turn on the shower and sinks, one at a time, and check if you get water draining from the black tank. This will confirm if you have what would be expected to drain into the gray tank going into the black.
Also consider measuring the capacity of the black tank by filling it with measured bucket then compare it to the OEM capacity. You can also check when the various level indicators come on. Full could be coming on at 3/4 or 2/3.