When you first turn the ignition switch on the engine computer will run the pump for a few seconds. That pressurizes the fuel rail which allows the truck to start. When it starts running the oil pressure switch takes over. Cold oil will hold pressure longer, as long as the fuel pump doesn't run excessive I would not worry about it. As for your original issue I would check the plugs & wires. You may even run a compression check. That said the question is how bad is the idle a domestic push-rod 4 cylinder won't run as smooth as an overhead cam engine.