No, not scotch tape! LOL. Cello tape like this:
Personally I don't like the way it feels, but it looks right on certain bikes.
The other period tape would be cotton tape like this:
Traditionally it'd usually be black, but you can get it in many colors these days from Newbaums.
Both these tapes are pretty thin. I use cotton on some bikes but I also wear gloves.
You could also do leather tape, that sometimes looks nice but it's expensive. Cork tape is cheap and almost never looks quite right, but it's comfortable.