Hah! Yeah, I don't think we need to limit "General Electronics" to strictly Arduino related or nothing.
How about this? It relies on only about 15uA pulled from the 5V supply to the base of an NPN, then that draws about 140uA through a resistor from the 14.4V supply. No other power when the 5V supply is present.
When 5V goes dead, the 2nd transistor gets turned on through the 100k resistor. This pulls the base of the 3rd transistor, a PNP, low through a 10k resistor and turns it on. lighting the LED.
The 10k from 14.4V to the PNP base is to make sure it is kept OFF when the 2nd transistor is OFF.
Edit: That first resistor should be 3.3M. Somehow my decimal point got lost... and 1.3uA from the 5V supply. I'd feel more comfortable with a slightly smaller resistor here, like 1M.
