Hi,after looking at your plug and your car being 2001 built,fitting the 04+ tail lights should be plug and play,because you have same plug,harness as the 04+ X5s.No need for OE adpater cables or pin swap,at all!!!!
It was only on 10/2002+ cars that Bmw changed the plug and harness as you can see form my earlier picture and also stated in retrofit OE instructions I am attaching here.As you can see,in the instructions,which cater for pre 10/2002 and 10/2002 cars,the adapter cables are not needed on earlier X5s.Sometimes its needed (see picture ) to trim a bit around the tail light location for fitting the 04+ lights!Did you have to do this on yours? Hope it helps
