Dear Bloody Snow,
I don't know how I can explain it better - difficult without being in person. The day tank is lower than the engine (and lower than the point in the system where the vacuum gage is located). The engine has to suck the fuel up against this height difference. Even when the flow stops the suction holds - the fuel is trying to run back down into the tank.
To further discuss other people's suggestions - the air has to be able to enter the system somewhere. Possibilities are:
1 return line to the tank - would require reverse leakage of the check valves in both the injector pump and in the lift pump (a total of at least 3 checks). Seems unlikely, but is possible. In the industry I work in we are told never to rely on a check valve totally sealing.
2 a "vacuum" leak between the day tank and the injector pump. This is interesting because from the day tank to the lift pump is always under a (slight) vacuum when the engine is running. This means that the engine would be pulling in air with its fuel. Perhaps this tiny amount of air is able to pass through the engine during running but the engine cannot handle the arrival of the accumulation of air which builds up during long periods when stopped.
3 a "one-way" leak between the lift pump and the injector pump, which only allows air in but not fuel out.
I think that option 2 is the most likely. I have personally seen air leaking into a filter set-up when subjected to a mild vacuum. If the leak is indeed between the day tank and the lift pump it could even be a bidirectional leak and no fuel dripping is seen because this system is always under a slight vacuum. You could try putting pressure on this part of the system and look for fuel leaks. It would be nice to pull a vacuum on the fuel line and watch the vacuum gage, but this would probably take a very long time to show anything. The transparent tubing suggestion sounds good as well but, once again, it would probably take a long time to see. Perhaps put the clear tube between the filter and the lift pump and watch for a slug of air at start up. If you see the air, the problem is between the day tank and the filter.
Nick (suffering from the sun)