Your tank must have a vent line that is open to allow fuel to be pulled out of the tank. Newer tanks all have a dedicated vent system but some of the older ones had a vent passage built into the cap. I am not sure which is the case for your trucks. The "normal" operation for the fuel tank is to deliver fuel to the engine but as that fuel is removed from the tank air must allowed to enter to avoid a vacuum being developed in the tank that overcomes the ability of the pump to suck fuel out to run the engine.
Storing with an empty tank does eliminate the potential problems of fuel degrading over time. To overcome any moisture accumulation in the tank from empty storage using gasoline with ethanol or adding a fuel deicing additive when you add fuel.
