Do any of the wiring sets/bundles have a tag wrapped around them which would have the BMW part number written on it?
The part database does give the wiring set part nbrs for the headlight up to 10/03 build date...but the diagram for the facelift doesn't list the wiring sets (the numbered triangles in the diagrams). You can walk in to a local BMW dealership's parts department and ask if they can identify or find the wiring set in their system. The BMW ASAP (after sales assistance portal) program may provide more specifics.
Again, the
pre facelift diagram/part number index does list items #21-#24....but if you enter a facelift e53...then the part number index doesn't list those part nbrs...BMW ASAP may, but you'd need to inquire at a BMW parts dept counter: