Close the gray tank drain valve. Open the black tank drain valve. Stick a water hose in the top of the vent pipe and turn it on slow. If water comes out the drain you've found the vent for the black tank.
BTW, the vent pipes are primarily installed to prevent a vacuum being formed when water runs down the drain. Without the vent, the vacuum would pull the water out of the p-trap then allowing sewer gases to come up through the sink or toilet. Thus the use of air admittance valves at sinks difficult to reach with a vent.