I am replacing the top on my 63. Convertible Guys sent a pad separately from the top. Was there a pad on the original. (I should remember, i had a a63 Fury vert...a long time ago!)
Do you mean like an insulation pad? Every convertible I had or saw did not have anything originally. The high end Imperials may have but I don't think so.
Fuselage models have padding above the side windows where the bows really curve down. I'd assume earlier models are similar. The pads are about 8-12 inches wide and 7 feet long give or take. They start at the header and end at the last bow.