the headlights are not supposed to come one when the engine is off, and it is obvious that your engine is off, when the light comes on...

The lights will come on from the iBus command, you can turn on/off each individual light in your car by sending a specific command on the bus - since your battery is dead and is laying on its deathbed, chances are that improper voltage level in the system causes the iBus to act unexpectedly, in your case activating the headlight...

You need a new battery