Got the same issue. I just put new lines at the tanks and clear plastic inline filters "before" the FSV and another clear filter where the FWS used to be so I could look for air. Put it all back together and "yay" it would work on both tanks all good to go...and then three days later air intrusion! The classic start for three seconds and shut off, and crank-crank-crank. Does the lift pump have an anti-drainback valve? The clear filter at the FWS location is full and I can see fuel pumping into it when cranking. But some how the filter is losing prime? If I take the fuel line to the rear tank off of the FSV it has great vacuum and will just keep pouring until you pinch a line.
It works just like taking the straw in your drink at the restaurant, putting it down in the glass and holding your finger over the end to seal it off, and then lifting the straw out of the drink. As long as you keep the end sealed with your finger, the drink stays in the straw.
That's how this fuel system in these trucks work. There is a supply line coming from the fuel pump on the pass side front corner, and there is a return line going down the back of the engine and back to the tanks. Everything on top of the engine must be sealed tight. That means all the fuel line fittings, the fuel filter gaskets, AND all the return line fittings. That would be all the little lines going from injector to injector, and the o-rings inside the injector return fittings. These o-rings are famous for getting old hard, and letting air in. When they have fuel running through them they may just seep a little bit and not cause a problem, but when the system is turned off it's doing the drink in the straw thing, and any little bit of air that can get in will let the fuel start draining back to the tank through the return system.
So look over the whole fuel line system for dampness, especially around the top of the injectors. The last time I had air intrusion it was the small line going from the injection pump to the return system. It was obvious, it was damp with fuel.
The red lines in the picture below are the return lines. Some engines have a little bit different routing though.
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and sure enough one of the return caps is bubbling! I just replaced all of the line and caps last Oct. The air intrusion blues makes me wonder why I love this old beast so much? 
