Back when I had some enthusiasm for dragging my video camera through caves once in a while, I came up with a lighting system that seemed to work OK at short to medium range. Sorry I don't have any photos of it, but here's a description if anyone is interested:
I used a Sony Handycam sealed in it's Sony Sportpack waterproof housing, to which I mounted a battery, lamp and switch. I bought a pair of small, egg-shaped 12 volt driving lights from Wal-Mart for about $15 (I used one, and kept the other as a spare). They use the yellow-tint halogen bulb with built-in reflector - about 20 watts, I think. You can also get clear replacement bulbs for them. The bulb throws a nice, flat, round beam - the only downside is that it's slightly tighter than the camera's lens, giving dark corners to your image when zoomed all the way out.
I screwed the light to the tripod mounting bracket on the bottom of the camera housing using a short stainless steel bolt. I wired in a toggle switch, and glued it to the small spotlight mounting bracket. The battery I used was a 12 volt, 1.2 Ampere-hour Sealed Lead Acid - I'm guessing it was about 4 x 2.5 x 1.5 inches. I made a little harness for it, which was attached to the hand-strap on the side of the camera housing. That put the small-but-heavy battery at the perfect balance point when using the camera hand-held.
The battery life lasted a whole 20 minutes or so, but of course I always carried a spare or two. The lamp gave pretty good light, and the whole setup was fairly compact and robust. Who knows - I might even get motivated to try some more of this foolishness one day...