fuel pump outlet line disconnect at filter turn key on pump 3 sec runs then stop

Hello, it is very likely that the fuel pump is only meant to run until the fuel system is primed. After the engine is turned on, the fuel pump should run until the key is turned off. It sounds like it is operating properly. If it is running at high idle, I would first suspect a vacuum leak. Is there any damage to vacuum lines, hissing, or a way to make the issue better or worse?