Interestingly the stone is formed as two pieces, looks like a lego connection inside, it might allow the LED to fit inside the stone.
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Very interesting. Maybe you could poke a needle up in there to fish around and get a general idea if it is hollow and how much room. If its enough for a light, then just drill a little hole in the bottom and voila.
Do you think the light would be obvious inside though? It seems to work so well just the way you have it.