Vargo was the home plate umpire for Sandy Koufax's no-hitter against the Phillies on June 4, 1964, as well as Koufax's perfect game against the Cubs on September 9, 1965.
From the AP obituary:
Vargo wore the same jacket when he worked Koufax's perfect game, the first World Series night game in 1971 and Hank Aaron's 714th home run in 1974. He gave the jacket to amateur umpire Ray Gouley, who donated it to the Hall of Fame after he learned of its historical significance.
The last game Vargo worked was the second game of a doubleheader between the Mets and Expos on October 2, 1983.