Trying to work out what circuit creates the ablity for warning lights to come on when the ignition is on, but the engine off - and then turn off if the engine is running, with the key in the same position.

Any assistance/explanation would be great!

Depends on the car and on the warning light.

Most warning lights will come on for a pre-set time interval (e.g. your ABS, airbag light etc.) and will go off even if you don't start the car.

The one that stays on until you start tends to be the alternator light. The way this worked on old cars is the light tends to be part of the energising circuit for the alternator, so when the alternator isn't generating power (i.e. engine stopped) the light is on. As soon as the engine is running and the alternator is working, the light goes off. This way if you lose charge with the engine running, your warning light illuminates.

Modern cars know they're running because the ECU registers RPM.

The charge warning light and the oil pressure light are the two primary non-ECU controlled lights that should be extinguished with the engine running. On a modern car the rest tend to be ECU controlled diagnostic lamps.

there is no circuit as such.....the alternator works by applying a 12v to the alternator which illuminates the light, once the engine starts the alternator generates the same voltage in reverse and the bulb goes out. (a bulb needs a difference in voltage to light up).
the oil pressure switch is just that ....a switch, normally closed (i.e. on) and once the engine starts the switch is forced open (i.e. off)