Mine, early 72K, (March 1960) I'm pretty sure came with the black vinyl wrap. I don't agree with everything Piggott says, but I think he's correct on saying that Standard-Triumph probably got their harnesses from more than one supplier. That would explain why cars made two months before and six months after mine had braided cloth wrap.
My POs only chose three sources for parts; Pep Boys, Earl Schieb and Sears, so I'm sure my harness is original. One PO apparently had the usual dirty/corroded connectors problems. So they went out, bought a roll of 16ga. red ignition wire and some crimp connectors. The last 6 inches of every wire under the hood was red 16ga. regardless of what gauge and color the original was.
At that time, I couldn't afford a new harness (if they even existed in 1987), so I removed it, laid it out, unwrapped the vinyl and moved the nice shiny PVC colored wires out where they could be seen. I then went to Pep Boys, bought a roll each of BLACK 16ga. & 14ga. wire and soldered in replacement lengths where they can't be seen. Moss sold the non-adhesive vinyl tape to re-wrap with. Still works.
Frank