Where does the 12V come from on the Prius?
The main battery on a hybrid vehicle is at a much higher voltage than 12 V. The 12 V systems are fitted to allow standard 12 V accessories without the manufacturer having to design the whole lot from scratch.
There does not need to be a 12 V battery at all. There could be a regulator from the main battery to run the 12 V systems even when the ignition is off. If so, the battery voltage may not change when the engine starts. There is also the added fun that the engine stops and starts on a Prius, so if the battery voltage does go up and down as the engine starts and stops, your circuit will switch on and off while you are driving.