I have some ESI bar tape that came with a very usable finishing tape. It is all silicone, so will be durable. The bartape actually has no glue and is reusable. Also very fat and grippy. I like it a lot. Expensive..
I did once use a heat gun and a ring cut out of a small fizzy drink bottle. just because I could. acts like heat shrink (which would also be an option, just plan ahead and fit it before you put the tape and levers on).
You can get rubber rings that hold the end together like tape - super tidy and last forever. The only issue is that you need to put them on the bar before you apply tape, and come to think of it before you put the shifters on…