I'm going from memory here since I sold my 90 Grand Marquis in 08, but if I recall correctly, there was a water connection which pressurized the main water system in the same bay as the tank drain valves. You filled the water tank by actuating a switch in the kitchen, and the water tank guage was on the mission control panel over the pilot's head, making it convenient to know when to shut it off. IIRC there was no automatic shutoff on the fill switch but there was an overflow pipe to avoid pressurizing the tank.
In the water bay there was a black tank rinse connector which was labelled with the name of the spray ball company. I can't remember the name, but the regular water connection wasn't labelled. An easy way to check would be to stand by the drain valves and drain the tanks, then turn on the water hose and see if one tank runs water out it. To confirm the source, close the water supply hose valve and see if the flow stops.
Another thing to consider is whether the low point drains are set right. My Grand Marquis had them in a small space under the bottom bathroom cabinet ....you lifted the cabinet floor to get at them. IIRC, there were both valves and caps to both hot and cold......connecting them backwards somehow could give you quite screwy results.