On my 2001 530D Touring, the offside sidelights/flashers operates intermittently even the ignition is switched off and the car is locked.
When the ignition is on, the flashers operate intermittently, sometimes for a few seconds, sometimes for a few minutes. When the ignition is off, the OS side and tail lights exhibits similar behaviour, as though the flasher switch had been left in the 'right' position to use the parking lights (a thoroughly odious feature anyway - the number of flat batteries I've seen due to that is anybody's business).
This still occurs after removing the steering column trim and disconnecting the big plug and the little plug from the flasher switch, the small plug from the wiper switch and the small central plug that appears to connect the (M sport) steering wheel buttons. I have not yet tried unplugging the ignition switch module.
Also, when all the plugs are connected, the ignition is off and the headlamp flasher is operated, the dip(!) beams come on and stop on until the light switch is turned on and off again.
As the car stood for some time during the very cold snowy spell and the windows are tending to mist while the car is standing, I suspect damp has invaded a magic box of some description and a quick squirt of magic box reviver might be all it takes, but I have no idea which one - there seem to be far too many for my liking.
This is one of those faults that goes away for a bit when you fiddle with practically anything at all, and then, just when you think you've finally sorted it (even though you have no idea what whatever it is you fiddled with has to do with the problem) comes back again.
Although I have some expertise with auto electrics, this is beyond me, especially as I am currently condemned to working outdoors.
I would be extremely grateful if someone could shed light on this matter!
(There are a number of other electrical faults too, such as the tailgate, but this one is currently the most critical as it rapidly drains the battery while the car is standing for much more than a day or so.)