“Koufax did not refuse to pitch on Yom Kippur. He was spared that since Don Drysdale would have normally pitched in the rotation that day. “
Never did Koufax pitch on Yom Kippur. He sat out important games in both 1961 and 1966, and the Dodgers lost both games.
Koufax had pitched on October 2, 1965, allowing 4 hits and 1 run as the Dodgers defeated the Milwaukee Braves, 3-1, clinching the National League Pennant. The World Series started October 6, 1965. Back then, pitchers pitched every four days and managers tried to get their best pitcher to pitch the first, fourth, and seventh (if necessary) games of the World Series. But October 6 was 10 Tishrei.
You may be thinking of 1966. Koufax had been scheduled to pitch September 24, 1966, but that was Yom Kippur; the Dodgers lost 4-0 to the Chicago Cubs and yet another future Hall of Famer, Ferguson Jenkins, still the only Canadian in the Baseball Hall of Fame. Koufax had pitched the last game of the season, the second game of a doubleheader, on Sunday, October 2, 1966, which the Dodgers needed to win to clinch the Pennant. They defeated Philadelphia, 3-1. (The losing pitcher was future Baseball Hall of Famer and US Senator Jim Bunning.) Koufax had also pitched three days earlier, on Thursday September 29, as the Dodgers defeated the St. Louis Cardinals, 2-1. Ordinarily Koufax would not have pitched on two days rest, but when it was win or nothing, you do desperate things. (The Dodgers had lost the two games in between, and Koufax had pitched and won Game 7 of the 1965 World Series on two days rest.) Drysdale had lost the first game of the doubleheader, pitching only 2 innings, so he started Game 1 of the World Series on two days rest, losing 5-2 to Baltimore. Koufax pitched Game 2 of the 1966 World Series on the usual three days rest and the Dodgers lost 6-0 thanks in part to some awful defensive play; the winning pitcher was a not-quite-21-year-old named Jim Palmer who would also end up in the Baseball Hall of Fame. Nobody knew it at the time but it would be the last game Koufax would ever pitch.