That's well observed, chrise. Was he doing the same things with either hand or was it one hand for some things and the other hand for the rest? I note the actor (Chuck Connors) played baseball in real life and he batted and threw left handed. Perhaps he pretended to be right handed when using a gun, say, because it was a better look on film.
I use different hands for different things and if I were to play cricket I would bat right handed and bowl left handed. I write left handed but use scissors, for example, in the right hand.