I have a 2002 X5 with the 3.0. I purchased the car used last year and the front reading lamps have never worked properly. For example, neither lamp works when you turn them on individually. However, if the rear dome light is on, both reading lamps function properly. When you turn the interior lights off the reading lamps will not turn on when the appropriate reading lamp button is depressed. I have removed the front dome and reading lamp assembly and all the circuits appear to be in good shape. Any suggestions?

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2002 BMW X5 (E53)