Spent a while this afternoon looking at wiring diagrams and tracing the wires in my K4 loom. Got some coloured felt pens and some paper, worked a few things out. I've finally worked out the relationship between the plain brown wires, the brown wires with white trace, the ignition and lighting switches, and the side and tail lights.
Brown wire supplies tail and side light.
Ignition switch in 'run' position, side and tail lights illuminate when lighting switch is in dip or main position. Brown/white wire from lighting switch is live when switch is in dip or main position, connects to brown wire at ignition switch in 'run' position.
Ignition switch in 'aux' position, side and tail lights illuminate. Red ( +ve ) wire in ignition switch connects to brown wire.