My 1993 XJ6 just came up with a problem that I have no clue
why. When I turn the car off, the bright filaments on the
front and rear lights come on. These would be for hazards
and turn/brakes. When I fire up the car, the lights go off
and function correctly. But when I turn the car off in
about 5 seconds the lights come on steady. When I hit the
emergency flashers they flash. So I have to disconnect the
battery every time I shut it off. Its like a relay is
acting up but have no clue even where to look. Please
help!!! Its not the driving lights or parking lights. Its
the larger filament of the bulbs. I have had a light bulb
failure light on for a few months while all the lights work
but this didn't seem to affect the operation of anything.

 

You say that when the car is running they function right. That is- they go off, and then on with the switch. I think I would be looking at the hazard switch itself and the electric side of the lock cylinder. May be there's wear in the ignition switch so it settles to that connection? Good luck.