Back before the advent of cushy bar tapes the bars were always taped from the top to bottom and would be finished with a plug or occasionally a bar end shifter. While it is true that the edges of the tape could and would roll, tape was inexpensive enough that this would be the indicator that it is time to buy new tape. It didn't seem so expensive back then, and most cycling enthusiasts did it themselves. Perhaps Tressostar and Velox were better able to bend or stretch to the contour of the handlebars than Neuman's. Since the brake levers don't have rubber/latex hoods, it was usual to put a wrap of tape around the brake lever body as shown in @
gugie 's post #10. This would make it slightly more comfortable when on the "hoods".
I am not against taping bottom to top, but I usually do that for the more modern tapes.
If I had that Bottecchia that @
Erzulis Boat has, I would tape top to bottom with Newbaum's cloth tape and tuck the ends in with rubber (Velox) plugs if I had them. This is just my opinion. By the way, I like that the bike retains the three pin steel crank arms. The paint looks awesome. I'm looking forward to seeing the handlebars wrapped. Whichever way you do it.
By the way, it's tape, it is meant to be replaced. Then you can try a different color or technique.