Your headunit was linked to your lights-on-signal-warning? I've never encountered that before.
Back when I was in highschool I purchased a 1976 AMC Gremlin that had been stripped, gutted, and raped. I had to redo the entire electrical system and came up with an awesome idea. Why not link my headlights to my ACC, that way when I started my car, my headlights would come on and when I turned my car off they would go off. I even hooked up a kill switch to it so that I could manually turn them off. This was before any of the Big 3 came out with automatic headlights or daytime runners.
Maybe you could do something like that? The only problem is that you would have to turn your key to ACC in order to have them on while the car is not running.
Or maybe you could rig up a relay to turn them off 60 seconds after the ignition is turned off.