I modeled this after the box art of the tabletop game Forbidden Island.
The tower is hollow so you can add a LED inside, the base has some room for a battery but it's not specifically designed for any particular setup.
There are files for merged whole model (still hollow) and separated roof options.
Funnily enough a LED tealight could be used upside down like in one of the pictures to make it look like a lighthouse! For that to fit better you should scale the model up a bit and print the flat roof option.
Only the roof cap option does need supports.