How do I build a DC time out circuit that stays off until power is toggled?
Yes, a 555 would do the job.  The 555 can work in a number of ways - the one you are looking for is called "Monostable".  This triggers once on the press of a button and turns itself off after a certain amount of time.  Nothing happens until you press the button again.

Replacing the button with a capacitor effectively gives you a single press of the button at power-on time and nothing after that.

Something along the lines of (though I haven't tested it of course):







simulate this circuit &ndash; Schematic created using CircuitLab


R1 and C2 define how long it stays turned on for (around 363 seconds that should be with those values).
C1 and R2 cause a delay on the trigger rising at power-on (you may want to increase C1 slightly for more initial delay).
The 555 when activated turns on Q2 which in turn turns on Q1 which allows the power to flow to the LEDs.


By the way, this circuit was inspired by: http://555-timer-circuits.uk/operation/one-shot2.html