I think a few folks have figured out how to control the backlight from the ignition power. It doesn't come that way "stock" as it complicates installation a bit, but it can be done with just adding one resistor I'm sure. [figuring...] Looks like about 300ohms+ and 1/4 watt+ resistor for the standard display. Disconnect the emitter lead on the pnp from the onboard 5 volts and hook the emitter to ignition power through the resistor.
In theory of course
But if it works then the backlight would turn off immediately when you turn the key off.