Should the light not exceed the brightness of the key light, or should I only worry about making sure the light separates the subject from the background, but not being too bright to the point where it blows out any fine details on the subject?
Exactly as you say. But keep in mind it's not a science, if you try things out you may find that what you thought you shouldn't do, in the end it works better and looks better than "following the rules". Lighting is one of those things where you keep trying things out and move things around until you end up with something appealing. So don't be afraid to experiment.
Sometimes it helps to color your lights differently to increase contrast. Hollywood loves to use blue and orange.
