Well...why not take the LED strip put and see if there's +12v being supplied
by the brake light circuit. If there is, and all the LEDs are out, examine
the LED strip circuit board for burned traces. If there's a big resistor,
check its not open circuit.
If no +12v, check the connectors and ground.
To the OP: Does the rear deck 3rd brake light work? I'm thinking maybe it
was added after the initial car purchase by the previous owner and they
didn't do the wiring. Usually the deck mounted brake light is disconnected
and it's wiring is used to power the spoiler mounted light.
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