99 Camaro DRL/Headlight Problem

Before the failure of whatever failed, I had always been able to leave my headlight switch ON, and it would automatically turn the running lights on during daytime and turn the headlights ON at night. Plus, the headlights would go off when I turned the ignition OFF. Now, the headlights stay ON, even with the ignition OFF. I must turn the headlight switch OFF in order to turn the headlights OFF. I have replaced the DRL Module, but that had no effect on the problem. The little light in the A/C vent flashes when the door is opened, even when the ignition is OFF. I think this is normal.

Can someone please tell me what has failed? Or can you tell me where to go to find the answer?