I started out by (carefully) destroying the lamp with a screwdriver and small pry bar. I threw out the plastic junk and kept all the internal parts.
This is the wall-facing side of the lamp, showing how I reassembled the 'guts' of the old plastic lamp in the new wood structure. Only the on/off switch required soldering; I had to completely unsolder the switch to fit it through the hole in the wood. I used heat-shrinking plastic tubes to cover up the solder work. For the other wires, I used plastic connector caps to join them back up. I attached the components to the wood with screws and staples. It's hard to tell here, but I mounted the metal reflective shield from the old lamp to the wood surface behind the bulb. Last note: I had to cut all the wires when extracting them from the old lamp's plastic housing. The key thing to point out here is this: if you try something like this, be sure to mark the wires very carefully so you can remember how to reattach them.
And here's a wider view so you can see the effect of the light reflecting off the wall behind my main monitor.So that's it. The entire project took about five hours on a Sunday. I'm waiting for the glue to completely dry before applying a coat of polyurethane to the front.
The most challenging part was figuring out the design: I wanted to create a very simple and functional lamp using only scrap wood left behind from other projects. Aside from my time, the project didn't cost a dime.
The tools I used to assemble the lamp included a miter saw (to cut all lengths and angles), a biscuit joiner (to join the two pine pieces and the feet to the base of the lamp), a drill (to create a hole for the on/off switch), a table saw (to cut a strip of oak for the top edge of the lamp), wood glue, and a sheet sander. For the electrical work, I used a soldering gun and some heat-shrink tubing, wire connectors, a wire cutter/stripper, and a few screws and staples.
I think it looks better than the original. It certainly fits in better with my wooden desk than did the plastic lamp. I may have to go and break the other lamp now.