I just arrived home after driving my 1987 BMW 325, at night. I turned off the ignition and the lights … and the main headlights remained on. Turning the light switch on and off again made no difference.
Cause: a stuck relay.
I opened the hood, held it open with one hand so it doesn’t fall on my head, and took the clear plastic cover off the fuse and relay box. It’s up high inside the engine compartment, relatively close to the steering wheel area.
I rapped each relay in turn gently with my fingers or knuckles, and when I rapped the light switch relay, the lights turned off as they should have done in the first place. It’s the relay that’s closest to the firewall, in the row that is closest to the engine.
I need to replace that relay, but this trick means that I won’t have a flat battery by tomorrow morning.