The UK wiring and the US wiring is the same - if you look at the US Aux kit and the EC Fog kit, the harnesses are identical part numbers - and there are not different main harnesses for different markets.
As far as the Schematic goes, the ONLY 3-way accessory connector on the bike is the Heated Grips connector (item 48 on schematic) - and the Aux lamps connector is a 2-way (58 on schematic) - unless that is a mistake and is really a 3-way but not marked correctly on the schematic (you would expect a 3-way to be honest)
The grips connector is for sure that Tyco/Amp Econoseal connector (with the yellow insert); the other one on the harness is a Tyco/Amp MultiLock type.
So I suspect that you have not found the aux lighting connector and additionally, the schematic is in error, it should really be a 3-way.
(It would not be the first error I'e come across!!!!!)
Here's something to verify you have found the Grips connector - that purple wire on that one comes off Fuse 3 for that circuit - measure the voltage then pull Fuse 3 - if it goes away, you definitely have the
The Purple wire for the aux lights connector comes off Fuse 1.
Also, whereas the grips connector has a Blue wire, the Aux lamps connector should be Blue/Black, originating from the switch on the left side control
The blue wire will be 'hot' with ignition on, so you would have no control using the OEM switch.
Keep looking around the area behind the headstock - has to be in there somewhere, believe you just haven't found it.