I don’t precisely remember when I completed my job replacing bar tape on handlebars. I think it was most likely putting tape on the Atlantis. Although it could well have been on the Tourmalet. I learned to put tape on much the way I pulled it off. It worked about as well as the original jobs did which meant sometimes very well, and sometimes a strange problem were the tape would unspool or untwist over the corners of the bars or the top of the bar, wherever my hands often rest. This last tape job was done by a very proud bike store mechanic on a complete bike overhaul. The entire job was worth it, and the handlebar tape looked spiffy. Over time the bar tape twisted and exposed bare handlebars.
Something was being missed, so this time I shot out to the Internet and avoided reddit subforums and other places where I often find the advice misleading (read evaluating information https://fs.blog/evaluating-information/ for a good explanation of why this might be so). I looked instead for a simple video, not designed to answer problems, just a tutorial on how to do it. I found it in this video from Park Tools that suggests tape should be wrapped in the direction of hand twist. Further, that the twist should change from the drops (which admittedly I never use) to the handlebars. More importantly it showed me how to accomplish that going by the handlebar levers.
I feel good about the solution and now can see how it works in practice.
Then I think I need new handlebar tape as mine is nicked in a couple of places. I am not sure if that was leaning or a parking drop somewhere.