Using a modified Fujifilm flash circuit from a disposable camera, it drives the CFL. Not very brightly, but it works. Then, there are two rechargeable AA batteries wired to a charger (from a Wii remote battery charger). Also, a small relay (in the normally open posistion) is wired between the batteries, so when the relay loses power from the adapter, it goes to the normally closed posistion, which closes the circuit and lights the CFL.

Or, in a simple short explanation:
Power on, batteries charge.
Power off, light goes on.