My comments are for the stock wiring harness, the S2 and TC harness should be very similar except for maybe the wiring color but should also apply to the British wiring harness
Both my S2 and TCS have four connectors, three dual and one single bullet connector for each rear light as the S2 wiring diagram indicates. Unfortunately the TC wiring diagram do not show the connectors. Assuming that the British harness has the same color as your original car, you should be able to figure out which wire goes where. The leads from the rear light assembly plugs directly into the female bullet connector on the harness.
On your picture of the connector with the two red leads, one lead provides power to the connector whole the other red lead is daisy chained to supply power to the other side rear light assembly. The side marker leads plugs into one outlet whiles the rear tail light lead plugs into the second. My picture shows the setup.