Cloth goes top-down. So does Benotto plastic tape. Everything else goes bottom-up. The following is my tape saga, a longer winded version of this. Continue at your peril

In my ill-spent youth, when cloth was king, gel was something you put in your hair, cork was whispered-about unobtanium, and Benotto plastic was for racer types whose hands sweated much less than mine, wrap jobs went from stem to bar end. I did it that way, and everyone I knew did it that way. It never dawned on me to do it any other way, and I never saw anything holding down the tape at the stem end. Not little strips of what looks like electricians tape. Not actual electricians tape. Not twine. And if you want padding on the bars, you used multiple layers of tape or <shudder> that foam rubber stuff that looked like what is now used to insulate outdoor pipes.

Of course, the cotton tape of choice, at least in my circles, was Tressorex or Tressostar (never did figure out the difference), which had adhesive on the entire backside of the tape. As others have said, it got ratty eventually, but it held down pretty well.

Once padded tapes. cork tapes, gel tapes, and the like came along, the game changed. The adhesive did not go to the edge of the backside of the tape, making edge turn-up more of an issue. Also, because it is thicker, you can't just shove extra tape into the bar end, willy-nilly, and whack the plug into place like you can with cloth tape - suddenly, trimming and some degree of manual dexterity and hand-eye coordination was required, attributes of which I do not have an over-abundance. That's when I started going bottom-to-top and learned that the average tape company includes the absolute minimum possible amount of finishing tape (for next to the stem), and make those strips with an adhesive that sticks most effectively to itself, making any accidental fold-over whilst handling into a minor disaster, all of which thereby makes life unnecessarily difficult for the mechanically declined.