I believe it was yclo who managed to stuff a bare-bones SatCure circuit in to the head of a Solitaire. That circuit would easily power either a single red or white LED off a 1.5V cell. The problem is building such a small circuit is really delicate work. Then there were other modders who managed to put in (IIRC) a Zetex circuit and run a LS in there.
But for simple bare-bones modding, a 3mm red LED, a 12V (MN21/23) battery, a spacer/ extended spring and a 0.125W current limiting resistor should be fine. I just don't like it because the 12V battery is harder to find, and I think the run time suffers too. (Someone jump in here and give the runtime??)
Your best and simplest choice would be to buy the Arc-AAA, or if you don't mind it a little dimmer but with incredible run time, buy the CMG Infinity. The CMG Infinity Ultra, recommended by Mark, is as bright as the Arc-AAA but comes only with a white LED, IIRC.
Arc-AAA: bright, AAA cell form factor, approx 5hrs bright before moon mode kicks in, moon mode for easily 5hrs more.
CMG Infinity: about half as bright, AA cell form factor, approx. 20hrs before output is equivalent of moon mode (doesn't actually have step change in brightness), should keep going till 40th hour.
My only grumble with these 2 lights is that I would like the option of having a protective lens over the LED that I could change out when needed.
I don't like button cell lights like the Photon II or similar for military purpose. They can survive dunking, but are not actually water-resistant. The cells are hard to change in the field. The runtime for actual useful light is a lot less than either the Arc or Infinity. Since they are push-on, they can come on at inconvenient times like when you are prone on the ground with a pack strap digging in to you. That said, I do keep a Photon II in a emergency pack (carefully positioned so as not to acidentally light up) because the lithium cells have an incredible shelf life and the light is very compact.