The cover sliding back and the lights flicking up would be easiest to do using a cam/lever design, that would require nothing more than some trial and error. An ideal motor would be a power window motor, or something like the geared motors that are in automotive power seats, they're designed to handle pretty massive torque and provide a slow smooth movement. Stopping the motor would simply be a matter of using limit switches. Could probably be done pretty easily with a visit to your local car junkyard, and a few bucks.