2002 chev pickup 4.8l fuel pump not always coming on with key = no fuel i jump prime connector and it works sometimes new pump installed already?

The fuel pump is controlled by the Fuel Pump Relay which is controlled by the Powertrain Control Module (PCM). It is really quite simple. If you check for power and ground at the relay, it should go like this: There should be one connector that has Battery power (B+) all of the time. This is the power circuit that feeds the fuel pump motor. The circuit that this feeds will have continuity to ground all the time (You can check this by hooking a test light to B+ and probing the connectors. The light will light up when it finds continuity to ground) - this would be the circuit to the fuel pump motor itself. Another connector will have battery voltage only with the key in the ON and START positions. This is the power circuit for the relay primary coil. (The circuit that operates the relay) Last but not least, one other connector will have ground momentarilly when the key is first turned to the ON position. It will only be grounded for about 2 seconds. It will only do this once in a key cycle. You will have to turn the key off for about 15 seconds and turn it back on to get it to do it again. This is the fuel pump relay control circuit to the PCM - this is what actually turns the fuel pump on and off. If these circuits are all working, then the only other cause would be a bad relay.