I harlequin wrap my bars using cloth tape. The process requires tightly folding back the tape to bring the other tape over. I don't think cork tape will hold up to the folding and refolding.

Also, it is hard to continue the harlequin pattern past the brake lever, so I usually wrap from the center down and from the end up, and meet at the levers. With cloth tape you can then put a strip of tape over the join and it looks nice. With cork tape, that would be too lumpy.

I suggest you simply wrap the bar with cork tape, in the usual spiral manner, then harlequin wrap cloth tape over that. I've done that on one bike and it looks nice, gives a bit of extra padding, and isn't overly thick.

It took me four hours to do my first harlequin wrap, so be patient and relaxed.