Before I wrap the Levi's bike... Did the imprints look like this in the 80's? Thanks!

Crap... The embossing doesn't seem to be visible on the ebay offerings...

I think it does, but maybe the old imprint was smaller?
I have issues with the newest cork tapes coming from Cinelli, made in Taiwan. It seems like the tape at the edges of the tapes are not as thin as they used to be, which results in an ugly bumpy appearance, when wrapped on a bar. The smooth feel and look that I really liked with the Cinelli cork tape for so many years is now gone. I have since moved on to other brand cork tapes so I do not get the bumps on my handlebars. Soma's "Zesty" tapes look and feel pretty good. A bit cheaper too.
Why couldn't Cinelli just leave what wasn't broken, alone??? First they take away the chrome finish from their bar end caps, now this bumpy look and feel with their cork tapes....

I bought my first Cinelli cork tape when it first came out in the early 80's. It had no embossing and was only available in the natural tan color. I liked it a lot. I replaced it a few years ago with the new Cinelli stuff, which seemed difficult to wrap evenly and looked pretty bad close up.

Thanks, I punted and spent coin on old NOS stuff... Whoo… It seems like every step in this is way more expensive than I estimated...

Hopefully, what you got was the old stuff, as it seems like the bad stuff had been around for a long time already.
I think what you need to find is Cinelli tape NOT MADE in Taiwan. Cause it looks like the tape got bad when they moved production to Asia. Maybe Cinelli did not bother to send over the production machines over and just bought what was available locally? Only reason I can think of why the quality went down on their cork tapes.

Old stuff wasn't embossed (as stated above). I now wrap with "sterile" stuff for my vintage that I ride. I think I have some from Specialized that is not too thick with decent edges, I then just use NOS bar end plugs.

Ack... This project is getting painfully spendy… Yeah, I'm the guy that is going to open that vintage sealed action figure to play with it...

FYI, cheap Profile tape is unembossed, thin (by modern standards), non adhesive, and comes with chrome[d plastic] bar plugs.

I think you are recommending I use a modern look-alike? If so, I would prefer that, for many reasons, but this is going to spend the lions share of its life on display/wall art. This tape doesnt have the modern Cinelli embossing, but does have a small but identifiable chevron stippling pattern on it. Restoration to period correctness is the goal (except for true vintage sew-ups, BF has convinced me to run from) on this bike, And, NOS AX-7300 hoods will be finishing out the bars.

Anyone have any tips for wrapping with vintage cork tape???

Carefully. Don't pull too hard. You don't want to break it. The original flavor was more cork and slightly less plasticky, IIRC.
Honestly I hated wrapping this stuff when it came out BITD. Never ran it on my own bikes for that reason.

I don't recall when embossing started, but for sure no tape was embossed with logos in the 80s.

I got some cork/gel bar tape from Planet Bike. Edges are thin and smooth, no embossing or adhesive and it looks/feels great on my '84 Pug.
Jon

Haven't tried Profile, but had good results with both Orbea and Fizik white tape last Summer. Don