This big lamp bone won't do much good there because it's root is in a place where the lamp doesn't have any joints.
I would solve that with two Locked Track constraints. The first one is for looking up and down. Parented to that is the second bone with another Locked Track to handle looking from left to right. Both are tracking the same target.
Here's the setup from Haunt's trick bag:
Bone 1 is the boss. It has a Locked Track with Z locked and -x tracking bone 3. It can only move up and down. The blue joint is parented to that.
Bone 2 is parented to bone 1. It has a Locked Track with X locked and Y pointing to 3. It can only move left and right. The red part of the lamp is parented to that bone. It doesn't matter at all how high bone 2 sits as long as it sits on the axis of the neck. It only rotates around the neck axis anyway.
Bone 3 is the target. One and two point there.
Bone 4 is there for convenience purposes. The root of bone 1 can't be in the middle of the lamp's head (bone 2 could be, but who cares, you'll hide them anyway), so there's an offset. Bone 4 has a Copy Location Constraint to bone 3 and a Copy Rotation Constraint to bone 1, so the tip of bone 4 is where the lamp is looking. You can make bone 4 unselectable in the outliner. That way you can't miss the target bone.
In the end, you'll only have two bones visible, possibly with customs shapes: bone 4, so you see the exact focus of your lamp and bone 3, so you can animate the head. Btw, Luxo's neck seems to be perpendicular to his head which makes things a little easier regarding his focus.