Keep green light to your right, red light to your left. They're only there for orientation.
As for "rules" just follow the same procedure that the NPCs follow: incoming flights take precedence over outgoing flights! But, at the same time, there is no "moving backward", even if we can, so an outbound ship that's already clearing the forcefield takes precedence over an incoming flight.
Take any "stick to the green side" rules with a grain of salt, and follow them at your own risk. Yes, two Cobra's fit next to eachother in that gate, but two Lakons are a different matter. Better safe than sorry, and follow NPC rules. Would've been nice, if there had been seperate entry and departure gates opposite one another though.