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.
Step 2: Starting Up . . .
So you have the wire in the shape of the place where the lights will go. This is going to be your 'positive rail' for the LEDs.
Then eat the apple.
Step 3: Let There Be Light!
Then get a length of hook-up wire (I made made the length of my soldering iron power cable, but the length is up to you) and strip one end, revealing the copper strands. solder this end to the hexagonal ring. This is the positive lead for the power.
Next, with the left-over utillity wire form another ring and solder the ends together. This ring should be a little wider than the first, wide enough to firmly loop around the outside so that the cathodes (the shorter leads) of the LEDs can be soldered on the this ring. Make sure that there is no connection between the LED pins or the two rings. You could use heatshrink or tape to ensure this.
Step 4: Power Time
Then get one AA battery, and solder the other end of its wire to its negative end. Get a small length of wire (10-15mm) and solder one end to the positive of this battery, and the other end to the negative of another. Continue like this until the four batteries are connected in series.
When that is done grab the other end of the positive wire, strip it, tin it and solder it to the positive of the last battery.
To hold the batteries and their joints together I suggest hot glue, or electrical tape, por bath. I did both, as can be seen in one of the below images.
Step 5: Just About Finished
All that is left to do is to attach the ring of LEDs to the iron, and stick the negative wire in an appropriate place.
First the wire: get the spare end of the negative lead, and a small bit of tape, and stick the negative to the iron, a little from the end, but leave maybe 20mm hanging out and bend this little bit away from the iron. See the relevant picture below (the one with the lights off).
Next, the lights: slip the ring of the top of your iron (preferably while it's off) and wedge it on the place you moulded to wire to fit (for me its the hexagonal bit. Fits nice and tight). Glue or tape it down if you wish.
Last: Check the circuit and make sure that the two rings are not connected to each other, and remove any short circuiting you may find.
Then whenever you are soldering and want light just press the negative wire onto the negative ring (the one the cathodes are soldered too, the outer ring) and Wahey!! You have light!!!