the original harnesses didn't use vinyl/plastic tape, which is a fairly recent invention - the change from the braided cloth cable coverings of the 40's to the tape-wrapped cables of the 50's used a type of friction tape, which is still available, but provides less electrical insulation than the modern plastic tape - the reason it appears to have no adhesive is the sticky stuff on friction tape doesn't hold up long, which is why you'll find those old taped harnesses have odd wraps on the ends that actually 'tie' the tape end so it can't come loose later - use standard electrical tape for function, use friction tape if you're after 'the look'
Bill