How can I continue a circuit from a light switch through a light using 12/3 cable?
Looks like posting it here was all I needed to sort this out in my head.

The wiring is a similar idea to wiring two switches to a ceiling fan with a light, using a 12/3 cable. Only here, I've got one switch for the light, and the other hot leg is tied in so that it's always on, not switched.

I pulled a 12/3 cable from the flood light box (wired the same as first picture) to the light switch, and wired it as shown in the second picture, which I'll post again below:

In case my drawing isn't clear, the yellow boxes are wire nuts, and the terminal at the lower left on the switch is the ground. The red wire (hot) is connected to the light.