My first ideas were great, but didn't work in practice. 

This was the lamp. It has a 240V to 12V transformer, a clamp, a goose neck

I say "this was the lamp" because this lamp went down the garbage chute to be with its friends, the other pieces of garbage.

20V from a 12V supply

The first issue was with the power supply. It was rated at 12V, but I measured 20-and-a-bit volts with the lamp off. This was discouraging because the DMN2004 MOSFET I was planning to use to switch the lamp on and off is rated for a maximum of 20V. 

500mA lamp consumes 40mA

The next problem was that the lamp was only consuming 40mA. 12V * 40mA = 600mW, which is far below its rating of 6W. I suppose this is the reason that it was such a terrible reading lamp. This was the final straw. 

I wasn't happy working with something so broken, so it went down the garbage chute and I made a new plan.

On Reflection

As I'm writing this up, I can see that perhaps the lamp was fine, but only the power supply was broken. I regret not being more patient. On the other hand, I did like my new design (see next post) and it's not like these things are expensive.