For some reason...you can't go by the orange shift light on the early e53 models. When this topic comes up...most early e53 owners say their orange gear shift (tranny range indicator) light stays illuminated...even after the 16 minute "consumer shut off" period. (when the vehicle goes into sleep mode).
For an understanding of the orange gear shift light (transmission range indicator light)...see the BMW info below about "
CONSUMER CUT OFF". Perhaps it will persuade you to "believe"...but in your case...it may not apply.