You might be referring to the slightly padded vinyl tape that was very popular during the early to mid 80's.
Ambrosio made a good one (Called "Bike Ribbon") that sold very well. They had a slight leather texture moulded into them to help with grip and and small holes for looks. "Cork" tapes eventually took over the market from them by the late 80's and good quality vinyl padded tapes got harder to find after that.
Not sure if Ambrosio reissued their vinyl tapes, but I have seen them sold at eBay once in a while, but could be just NOS and not brand new....