Harris switch-pitched on September 28, 1995, the penultimate game of his career. His previous requests to switch-pitch had been turned down by his teams. While with Boston, his manager told him he could switch if he was able to throw 7 out of 10 pitches for strikes in warmups. He was able to do it, but he still was denied permission. There were other switch-pitchers in MLB in the 19th century, but none did it regularly (despite the old, errant listings of Tony Mullane being listed ‘TB’ for threw both.)
MLB came out with guidelines (not actual playing rules) for umpires to use in case Harris were to switch-pitch. Those guidelines specify that the pitcher must pitch with the same arm for each at bat. (A batter may switch boxes after every pitch up until the pitcher is set to pitch.)