Thiis is a weird one. If the cap was not vented, while driving it would create a vacuum inside the tank and not a pressure. As the fuel is sucked out by the pump air has to be able to enter the tank through the caps' vent to replace the fuel being taken out. If the air cannot enter the tank it will build up a vacuum. And eventually the vacuum in the tank will be equal to the fuel pumps vacuum and the fuel cannot move.
How can it be running out of gas, bone dry empty and then running out of the filler after the fuel sits and expands, and supposedly were only dealing with four gallons in the tank. I can understand running out of gas with only four gallons but not running out of the filler. What does the gas gauge say when its supposedly full? There are contradicting things going on here that do not make since at all. Check to make sure the exhaust is not heating the fuel in the tank and expanding it, that could explain it running out of the filler but not why you can only get four gallons in the tank. It just seems to me like you have multiple problems going on. The gas gauge can't possibly be working or you would not be running out of gas.
Why would four gallons of gas be all that will fit in that tank? That is weird! Was the manufacturers' shop cat a sleep inside the bottom half of the tank when they welded the top half on? Is four gallons all that will go in until the gas pump nozzle clicks off or is four gallons all that goes in until the tank is full to the top? Some tank designs are a pain in the butt to fill without pressure developing in the tank and causing the gas pumps' nozzle to continually click off. We had certain trucks at work that did that. On those I stuck an ink pin between the nozzle seal and the filler neck so it would not build up pressure.
Modern caps "non-vented" caps are still "vented" caps. The difference is they have an inlet valve that opens to let air flow into the tank when it starts to develop a vacuum as the fuel is removed and they have a pressure relief valve that will open if the gas expands on a hot day and creates too much pressure in the tank. The expanding fuel could be forced out into the EVAP charcoal canister and saturate it. Under normal operation these valves are closed which prevents the hydrocarbons from escaping into the atmosphere. Old gas caps like the ones on Early Fords and Mustangs just have a little vent hole in them sometimes its hidden in the caps construction and hard to see. True non-vented caps are usually heavy brass caps with a thick gasket. They come from the 1910s brass era when you needed a sealed system and a handpump so you could build up pressure in the tank and push the fuel to the carb. You closed a valve, and pumped up the pressure, and then continued to give the handpump a stroke every once in a while. Then when you stopped you opened the vent valve and released the pressure so the carb couldn't possibly flood over.
Jack Calori, that had a record setting flathead dry lakes roadster in 1947, which he also drove on the street with only hand pressure pump. Used a very old, teen era brass Cadillac gas cap to seal the tank. He told me that on a hot day, with a full tank, the fuel would expand enough to create its own pressure in the tank, and you didn't need to pump the hand pump at all, until the fuel level started to drop. Then you needed to give it a little pump everyonce in a while to keep the pressure up on the gauge.
