As mentioned in post #4...they also have a 2002 e53 X5 and the orange light never goes out on his e53.
This has been discussed many times over the last decades because it appears that early model years of the e53 seem to all do this...which is not the normal operating parameters of other BMWs of the same generation.
Later model years of the e53 tend to comply with the orange gear shift light turning off after 16 minutes (my 2006 e53 does)...but again, if you search this topic...you'll read that many 2000-03 e53s orange light never turns off...and we don't know why except BMW must have designed it differently.