once it's clean- or cleanish...
with both tanks empty and valves closed...pour a couple of gallons of water in the black tank.
see if you get drips overnight...put a pan under the drain.
then empty that tank
and pour a couple of gallons of water in the grey tank
see if you get drips
once you figure out which tank is leaking ( or both) you can service the gate valves
here is an overview of how typical systems work