Way ahead of you here.. I've been thinking about this since last night..

Just hook up a relay which gets it's input from the wire on your ebrake (used to light the dash icon that your brake is on) and then have that relay turn on/off your LCD depending on when the ebrake is on or not...

.... THEN (here comes the illegal part)

then you wire up a switch between the ebrake and the relay which is a SPDT (single-pole, double-throw), so that way you have two inputs which share an output. One input is from the ebrake wire and the other is from your ignition or carputer. This way you can override the ebrake if needed and flip it back when you get pulled over to "prove" to the officer that it will only work with the ebrake on -- if you get asked about it, of course.

I'm planning to do just this. Seems simple enough.