With my proximity type fob if I turn of ignition (aerial round switch barrel), and remove keys the mobiliser arms with seconds, so by the time I am out of the car, sorted out gloves and wheel etc its armed, then just remove FIA cutoff,
when starting car put in cutoff turn on and immobiliser is still armed, when I first got the car I thought the Immobiliser was disarmed when I switched cutoff to on, but after some tests, ie keeping proximity fob well away from ignition I realise I was mistaken, almost seems like the aerial for immobiliser was super sensitive for a couple of seconds after cutoff was powered on .
Tim