I'm not sure what size of capacitor you would need, but if these LED's are drawing low enough current, you could just put a capacitor in parallel with your LED/Resistor. When the 12VDC goes away, the capacitor would continue to feed the LED till it ran out of juice (It would even give you the slow fade effect). Just an idea.
I also you could check out this idea: Just look under "Power off time delay".
http://ourworld.compuserve.com/homep...wden/page2.htm