Well, I came up with a solution.
I got 6 bright white LEDs and stuck them on my soldering iron. Now I get light wherever I want it!
Note: just in case you are interested, this project cost $26.70 - and that was the cost of the 6 LEDs.
I excluded the cost of the iron, and all the other stuff included I had lying around. If you don't want to spend $26 on white LEDs, then buy a bright LED torch for maybe $10, and get the LEDs out of that.
Step 1: Parts
-soldering iron (whether it is temperature-controlled or not is irrelevant. Mine is a 25W Nicholson)
-6 bright white LEDs (Mine are 8000 MCD I think, but this doesn't matter)
-some bendable yet strong utillity wire
-normal hookup wire (not single-core)
-4 AA batteries
-wire-cutters, pliers, etc.