When I created the bones for my lamp, I kept them disconnected (IE “Make Parent”->“Keep Offset”). This was really useful give the design I chose for the various joints on the lamp. It worked great with rotation constraints, but once I got to this lecture on auto IK, my bones wouldn’t move together as expected.
I made a variation of my scene, but with bones filling the offsets. This worked with Auto IK. But it doesn’t feel like the “right” solution. I have a feeling there are some IK constraints to learn about relating to disconnected bones.