Some systems only allow the pump to run for a second unless the motor is running or being turned over. So what you are hearing may be normal. Apparently there is a pump power test lead located behind the left wheel between the chassis and the floor. This should tell you whether the pump is getting power and when. But if you are hearing it start, then it must be getting power. What you need to check is whether it keeps on running while you turn over the motor. The fuel pump relay is triggered by the ECU. The power from the relay then goes through a fuse and to the inertia switch and then to the pump. The test lead mentioned earlier is after the inertia switch. I would guess that if you applied power to this test lead the pump should run.
I hope this helps.
I hope this helps.