Turns out the bottom part is hollow. Hollow enough for the LED from a tea light, anyway.
This is a D&D Miniatures fire elemental, probably listed as some synonym for "really big fire elemental". Unbasing this guy was a pain - there are several pegs involved. Easiest way is to drill several holes in the bottom and break the base in half. He isn't as nice a technical sculpt as the Reaper model. but the light can go a lot further up and the orange is more convincing than the Reaper red.