A garden-variety solar cell (2-volt, 20mA) is all that's needed, and the entire circuit consists of ten basic components.
Step 1: The Parts List
BC327 PNP transistor
BC337 NPN transistor
1N914 or 1N4148 Low power signal diode
100uF 6v capacitor
100uH inductor (A larger can-type is chosen for its lower internal resistance. Thanks to acmefixer for bringing this up!)
1 x Red LED 20mA
1 x White LED 100mA. A wide angle unit (90-degrees or more) is recommended here to avoid glare and hot-spots. I also chose the piranha style so I can get the 90-degree angle when I assembled it.
Connecting and Mounting hardware.
Step 2: Assembly
Allow the space but do not solder the transistors till the very end to avoid any heat damage to them.