When you get a new modern package of wrap they come with pieces of branded vinyl tape, like electrical tape which is, according to the instruction sheet, supposed to be used hold down and finish the near the stem after starting from the bar ends.
I thought that a different way when I re-wrapped a couple last year. Before that, I hadn't done it in many years.
I found many wrap versions have a tacky underside also... yuk
When young I was strictly taught to do it starting from the stem with the tape holding itself down on the first two turns, always wrapping forward. Then to overlap a third of its width till the ends are tucked inside the bar end and the end cap holds it all tight to keep it from unravelling. No need for adhesives. I did it that way on a Le Tour last year with cork tape and on the Super Sport I sold not long ago.
I never did it a lot, maybe a dozen times, but if their were lever boots, I was taught to go under them. If no boots, then over the clamp and edges of lever body to smooth it over, just like on GTs58's Varsity up there. That looks like a perfect install.
Also deemed important was the direction of turn. Opposite of each other on each side of course but do the edges of the wrap allow easy non-skid movement of hands to the outside without feeling the edges. (wrapping forwards or backwards) But some folks like it "backwards" that way.
Looks like there's more that one way to skin a goat.
I feel comfortable with the no adhesives way like on the instruction sheet above, but the under/over the lever clamps did make me think on the SS when I was doing it because if you want to change lever positions later, and you have wrapped over the clamps, it all has to be removed to do it.
I wrapped it clean on the SS but I think if I was to keep it, I might wrap it first then put the levers on.