BMW X3 turn signal problem
 

My 2005 plate X3 is having a weird indicator fault. With the engine not started but in position 2 indicating left or right work fine. If I remove a bulb the MIL lamp lights up and the turn signals flash rapidly (As they should). If I start the car and indicate left the Mil lamp comes up and the turn signal flashes rapidly as though a bulb has blown although all bulbs are lit and OK. Hazard warning switch over rides the fault and causes the lamps to flash at the correct rate. If I turn the engine off when indicating left, the indicator starts flashing at the correct rate. Any help with this would be much appreciated as it is really annoying me........

The bulb may not be ok. I had a similar problem on my previous 325 where the rapid flashing would be intermittent. Turned out that the filament was actually cracked and would normally make contact (ie be closed) but over bumps or in cold weather would spread apart. Replacing the bulb would confirm this.