Your right it has nothing to do with the glow plugs as you have a petrol. As do I. Its to do with the power having to cut off from the Acc Socket / Cigerette lighter socket when the engine is in turn over. When you turn the engine to the point the dashlights up eg position 2, or when you press the start engine button in modern cars the following sequence happens.
The key or ignition is turned on by turning the key or pressing the button.
The power is provided to all circuits apart from the starter motor trigger.
When the key is turned to start the engine, or in push button cars when the ecu decides the car is okay and it can turn the engine over, the power is cut from all unnecessary items. This includes radio, Head Lights, Acc Power sockets, Heated screens, and all-sorts of other items light glove box lights. it depends on the car but most cars do this.
The camera does this during this process ...
It receives power and starts up.
The car begins to turn over. and the power gets cut so the camera starts to shut down saving all files and making sure it is safe to turn off.
While the camera is in the shut down process takes a short while, the starter has started the engine and restores power to the camera.
The camera shuts down but the power has not changed since shutdown. thus it stays off until you unplug it and plug it back in.
I hope this explains the process. when i say most cars do this. the only ones that don't are electric cars, and some with older constant 12 volt supplies. Cars with auto start stop technology will have this problem every time you stop at the lights.