Can you post an up-close picture of how you did this? I'm interested in doing this as well. Most of my reading time is in bed right before I go to sleep for the night.
I modified this by using gaffer's tape. It's a matte tape that can be removed and doesn't leave any sticky residue. With the modified version, the sticky part of the tape doesn't bend around the end of the arm at all. I cut this at an angle so the sticky part is only on the straight arm, so this does not interfere with it completely closing now. The flash on my camera is awfully bright and makes the tape show up a bit more than it really does. In "real life" the matte black tape just blends into the light arm itself. AND... what I found last night, even with the shinier black duct tape, the flap doesn't even show up in a dark room.
This is the light closed.

Here are a few shots of it open.



