A YouTube video of LM in court, at the 10 minute mark, shows Luigi signing with his left hand. He seems comfortable, not faked, to me. https://youtu.be/oCMXJW0g4Pg
The killer seems to have mostly shot with his right hand. I won't post that video because it includes a murder.
It makes me wonder if Mangione is "sheep-dipped" like is explained in this excellent video: https://corbettreport.com/episode-305-the-secret-life-of-timothy-mcveigh/
I don't know if this is news to anyone here, I'm not really big on this sort of thing. But when I watched the court video, I noticed he's a lefty and then I felt like I've seen this show before. Perry Mason, Matlock, whatever. At some point the lawyer throws a ball at the defendant and he catches it with his left hand and the crowd gapes.