I saw an interview with him on UK TV a bit ago and they asked him about this. The story goes that he had to have a minor operation on his throat, and as a result, he physically could not speak the following day, which happened to be a Saturday. However, he found that the experience of not being able to speak was very relaxing and meditative - sort of took him out of all the hubbub and hullabaloo of daily life. Over the next few days his voice steadily returned and he was fine by the following weekend, but he decided not to speak on that Saturday too, such was the experience of peace and quiet that he had had.
He basically kept up the habit for the rest of his life. He wasn't an absolute fanatic about it - if someone asked him if he wanted a cup of coffee he would say "yes please" or "no thanks", he just consciously tried not to speak on Saturdays if possible. Kinda unusual, but not very bad.
Hadn’t heard about the throat surgery - not remembering, anyway.
Well, I guess the not speaking 1 day a week is
on the less kooky side of strange things people do.
Maybe Hagman wasn’t in public much on Saturdays. . .