Buzzing noise seconds after ignition is switched on

[JorEl]

I recently purchased my Mk1 2004 3.6l Tuscan and in the first week or so of driving it I always noticed a buzzing noise coming from behind me a couple of seconds after switching the ignition on before turning the engine over to start.
I thought this was the fuel pump and was almost positive that I read that the fuel pump makes this noise and it can be heard inbetween turning the ignition on and turning over the engine.

..problem is, after driving the car for a few weeks now, I no longer can hear the buzzing sound when the ignition is switched on. I can leave the ignition on for 10 - 20 seconds and I could a pin drop, upon turning the key the engine starts everytime.

Can anyone please advise? Am I paranoid?