I agree that acting up after 20 minutes is a clue. Not too much of a clue. Can mean what others have said, venting, vapor lock, floating tank debris, loss of pump pressure/suction. The WWs I've had all have cable operated chokes. Maybe he will answer the questions in order for us. 50 guesses does not give someone a direction. No info does not give us a chance to use our experience.
The problem with the pump tests, is that 20 minutes. The truck is going to start with any of the pump tests. I have, and others have, run a truck with a hose stuck in a gas container on the passengers floorboard, hose thru the firewall. This way you can drive for 20 minutes to see if pump begins to fail or carb somehow fails. Idling for 20 minutes is not fool proof. Need a load. This is what Jerry already said. That would be a good easy test and give lots of info. It sounds dangerous but what the h e l l.
Anyway, this is all guessing, if it was debris, it would be at the bottom of tank near the pick up, after sitting. A person could say that is when it should "buck"/starve for gas. Not after sloshing....