Interesting, never thought of it this way. I guess a deep dive into TG is due. As things stand, there are records by Coil and Chris & Cosey that I rate higher than TG.
Yes, Sinatra was held in high esteem by quite a few of the postpunk crowd, including Robert Smith who was a huge fan of his phrasing. The man could really carry a tune...
Anyway, a lil something from my favorite percussionist of the postpunk era
https://www.youtube.com/watch?v=qnNJcm7uRFU