The engine power-off sound is played when disengaging the starter. Maybe I'm doing it wrong, but I don't think the starter is required for more than a few seconds and oddly enough the sound only plays when starting the engine the first time.

1. Start the game
2. Power on to batteries
3. Starter on
(ticking sound plays)
4. throttle to idle
5. Starter off
-> engine power-down sound plays, yet the engine is running idle.

if you repeat these same steps after landing, the power down sound no longer plays.