did you say the indicator is on too cos i no on beemers it'll leave the parking lights on is it just the one side thats lit up, try turning the signal off and see how you go, dunno how it is with the new mondeo's but parking lights on mk1-2's are on the light switch next the the steering wheel and you push it and turn it one notch back past the off position.

edit just read it's a 93, yea check your light switch, im about to clean the car so when i'm out i'll see if the indicator being on makes it do this i'll let you no if it does in a min