Never having had the combination of an original Ariel wiring harness AND a brake light system on a rigid / plunger bike I don't know for certain where the wires to the brake light switch ran. My strong suspicion is that they ran down the upper rear tube, past the rear fork and then down the lower rear tube to the brake light switch. The cables were held to the frame with spring steel clips, available from the Czech boys, amongst others. I have a few original clips here and from them I can confirm that originally they were coloured to match the frame colour.
I did enquire about having some made and then powder coated the appropriate colour a couple of years ago. Costs are not excessive but it is definitely one for the purists.
PM me if you are enthusiastic about having some made and powder coated.
36 4G, 37 VH, 53 ex ISDT KHA (project), 54 KH(A), Healey 1000/4 (project)
Former Machine Registrar & Archivist, General Secretary and Single Spares Organiser.