Alright, I opened the light up. Looks pretty simple except that a piece broke when I opened it. I tried soldering it back together, but it turns out that soldering copper isn't as easy as it should be.
However, how does the light turn on when the hood is opened? I don't see any moving parts, or parts that normally would have moved. The positive comes in and has a clip on the end of it (the part that broke off) and it goes around a bullet shaped piece that goes into a clip. I've attached a picture.
I figure that if all else fails I could just clamp the positive wire coming in to the positive circuit in the light and then wire in a switch, but I like to make things work as they originally did. If anyone can help me figure out how the internals of this work (AND how to solder copper together), I'd appreciate it. Thanks!