Ignition power for the brain is through the ribbon cable that runs from the Relay Sattelite to the Brain. Your asking how the brain knows when the ignition is on or off?, or if the engine is running or not. It'll know if the engine is running or not through the tach wire. You can get tach signal behind the cluster btw, one less wire to run through the wall and engine bay. It's the blue wire coming out of the harness closer to the tach side of the cluster.
I'm going by my Avital 4400 install manual for info on how your Viper hooks up. They are both DEI product, and both alarm/remote start combos, so the way they hook up should be nearly identical. I like your blue remote better than mine, lol.