That would seem to work if I could just use one point, then "wiggle" it around, possibly. But I don't understand the expression enough to know how to adjust the speed that the null moves around, and how I can make it move in more of a gyroscope kind of motion, if I want it to. Any thoughts?
That's EXACTLY what I've been playing with now. I had thought I wouldn't be able to get the global position value of the null if I did that, but thanks to another of your expressions:
L = thisComp.layer("Null 1");
...I was able to! Now I'm just creating a set of sliders so I can adjust the value of the radius and various properties.
I thought there might be a way to just do all of this without parenting, only using expressions. But parenting a null to a "Center" null with rotation definitely seems to give me the control I wanted. It doesn't quite move in a gyroscope-ish way, but that might be a matter of me tweaking the values more. Thank you for your help!