Perhaps you mean in parallel. An LED is driven by 20 mA, whereas a camera requires more like 200 mA, so it's not feasible to wire them in series - either the LED will burn out or the camera won't power up.

Yeah, I was pretty sure I was being a little sloppy by using the term "series" (for shame, physics prof, for shame!), but I was hoping to evoke the general sense of "if current doesn't flow through the LED for any reason, the camera can't turn on." Honestly, I'm not 100% certain offhand of a way to wire that (which is why I didn't want to be specific earlier, despite using a specific term: shoulda added some weasel words :) ). Do the LED and the camera run off of the same voltage? (If not, then parallel wiring won't work, either.)

>I had always assumed that the power for the webcam was literally in series with the LED

If I were tasked with making a webcam circuit, I'd make sure the light and the sensor were always powered together. So I (naively) assumed that's how everyone would do it.

Maybe you could add a capacitor to keep the LED going for a bit longer after the power cuts. The power off dimming might be aesthetically pleasing too.

I'd had exactly that thought. (Of course, the danger is that it might also lead to the LED taking a few moments to light up.)