AS Gillott - King of Rats in for a (Light Touch) Rennovation

Cinelli introduced cork back in '87 so if you don't really need to worry about "period correctness" before '87 the only padded tape (other than grab-on sponge sleeves and their cheap knock-offs (e.g. elan)) that I can remember was the Bike Ribbon Professional http://www.chainreactioncycles.com/Models.aspx?ModelID=27993 I used some recently on a bike and was really impressed.
(They also made a "fade tape" graphic which might work well on an '80's bike)

Back in the day I had the shiny Sellotape "Benotto" stuff, and also some faux-velvet soft-tape (mmm nice), as well as cloth, sponge and a nasty plastic tape that looked a bit like Nylon pallet ties with. Pimped bikes in the day also had sew-up leather sleeves on the bars (mmm nice)
reminds me of the 1987 freewheel catalogue. I'm sure they would be perfect on a Rossin with a Shimano Sante groupset.