PART NUMBERS
There are several types of lead according to the year of manufacture and / or the lead's original purpose.
(a) The short lead: 61132316621 BUT CHECK THAT IT FITS YOUR BIKE - BuMW CHANGED THE SOCKETS SOME TIME BETWEEN 04 AND 08.
It is, apparently, a lead that was originally used on the RT, not GS ranges.
I get the impression that there is no short lead alternative for more recently registered bikes.
(b) The long lead:
Basically, this is a much longer lead (it can be shortened, of course) that normally goes from the standard aux socket under the seat to power the optional aux socket on the beak. Again, there have been socket changes.
There are at least two alternative part numbers:
(i) Pre-57 plate: 61127700005
(ii) 57 plate onwards: 61127712581
So, the rule is check that you have the right lead.