if your budget is largish, how about this
1) a lithium coin cell or a pair of aaa batteries for 3v
2) an led or two of chosen color
3) a small atmel or microchip microontroller
4) assorted bits of wire
the microcontroller will sense ambient light presence using the LEDs which also double in their role of illuminating the pull (as cabinet / drawer handles are called here in the states)
ambient light = yes, leds in standby, unit draws a few microamps
ambient light = no, leds pulse (faster than your eye can see), alternately illuminating the pull and checking to see if the lights are on, unit draws roughly 25-30ma per led (as limited internally by your uC)
should last many many weeks
batteries hide on the other side of the drawer front or door, as guru suggested.