That is to say, a 3-level capacitive touch-switch lamp-dimmer was already partially-built into the arm of our chair: The metal tray support fixture
Okay, it uses one of these capacitance touch-dimmer switches... available at most hardware stores..
These are made to convert any lamp into 3-level touch-control. You just plug it in and mount an attached round metal disc (not shown above) wherever you want to control the lamp.
The trick with this project is to cut off the metal disc and attach the end of that wire to the underside of your metal tray support fixture:
1. Turn your chair on it's side, and look up inside the arm (with a good flashlight) at the fixture bolt. Attach the wire to it. Almost any method will work, there's practically zero current in the wire. I chose to crimp a 1/4" round lug to the dimmer wire, and attached the lug on the bolt with another nut.
2. Turn your chair back upright, plug in your lamp and you're done.
We use these with a small spotlight above for typing, eating etc but it's good for any frequently used light control.
Here is the actual switch model: http://www.touchandglow.com/product-p/t-300.htm