Do they still supply these somewhere? If not, is there some viable alternative method of battery replacement? I'm fairly handy with a soldering iron, and can easily MacGuyver the connector onto a new battery pack if I know the specs of the battery and the light itself.

post more info. What model? What does it say on your current battery?

It's the model with the gel battery (lead-acid). It says SB 3.2-6 (don't know what that is), and it's rated for 6V 3.2Ah.

Theoretically, couldn't I use a higher voltage battery and get more power output to the lights? Assuming that it doesn't blow them, of course. I'm pretty sure that there aren't any fancy electronics in the lamp.

You don't have to blow the lights to overheat something important. I would keep the same voltage.

If you can solder the connectors, look into buying or making a 6V RC battery. 3.2Ah is pretty big, but a quick search turns up some NiMH batteries with similar specs: https://www.all-battery.com/6v3800mah...connector.aspx

Haha, that battery is actually bigger. I figured that I could do that; there's a fuse on the lead-acid battery, but I assume that's because the battery is kind of touchy. I don't see why the headlights would need the fuse (other than a freak current overload).