Earlier quoted context omitted.
For what it's worth, you could just power on the camera, take a pic, then turn it back off instead. Provided you can do this fast enough, an indicator LED is rendered worthless. So you'd need to make the indicator LED staggered, to stay lit for a minimum amount of time. There's also the scenario where the LED or the connections to it simply fail. If the circuit doesn't account for that, then boom, now your camera can…
LEDs are diodes. So you can run power _through_ them. Power Supply -> LED -> Camera.
More also you'd want a hold up time for the light (few seconds at least), as taking pictures would flash them for 1/60 of a second or so.