So how does the automated system know whether my phone is dangling off the hook/cradle, or being held in my hand but I'm saying nothing?
Oh dear I fear a spat arriving soon.
It is simple. If you dial a number the system says you are engaged even if the connection has yet to receive a response and you just have the phone in your hand.
If a connection is made you are engaged until one of the participants ends the call. At that time the system regards you as off the hook after a given timing (pre-set) which also triggers the howler on your phone handset to prompt you to replace the receiver.
As previously outlined. Off the hook also displays a yellow light on the switchboard and engaged gives a red light
If you dial a number that is engaged you get the engaged signal on your hand set. Should your phone be siting idle the switchboard shows a green light. (inactiv)