That’s an unusual soft top. Early Dualmatic top maybe?
https://billings.craigslist.org/cto/d/1948-willys/6629924346.html
“48 Willy’s runs great starts every time and is reliable. Has had normal oil changes and tune up recently and has newer battery. It has a good soft top and doors zippers could use some work tho. All lights work but blinkers need work bulbs are good could be flasher or a little bit of wiring.”