Sorry for the late response. My guess? Shooting left-handed ...
[I also noticed when he punched the sheriff at the end, he did so left-handed; I believe he's right-handed, so I'd wondered at both moments if the scene was "mirrored" by the camera. FYI -- I saw a "nitpick" on a site noting that in "Unforgiven" 2/3 of the way through the film, the scene showing Eastwood and Freeman hiding in the ledge at night holding their rifles was mirrored by the camera, because Morgan Freeman is left-handed (but he was shooting right-handed) and in the same scene, Clint Eastwood was aiming left-handed (when he is actually a right-hander.)]