Do the mirrors have cutout sensors on them? If you run them out, does it stop and the current stop flowing? Also does it do that when you bring them in?
You could use a microcontroller that is timed to run them in and out. Use the ignition wire to signal when to run them in and out. But you would need a programmer to program the microcontroller. So you already have the relays setup?
You would need a regulator to limit the power to the micro, use a 12F675 (or 12C629) to a transistor to drive the relays.
Can you draw up what you have in paint and post it?