Many may remember him from "Designing Women," where he played assistant Anthony Bouvier.
Taylor had fought a terminal illness and faded markedly in recent days. His wife, children, grandchildren and mother surrounded him as he passed away, Binder said.
"It is with love and gratitude that we sorrowfully announce that our darling, amazingly brilliant and dynamic, Meshach, the incredible father, husband, son and friend has begun his grand transition," the family said in a statement.
Taylor made his screen debut in the 1978 movie "Damien: Omen II." He has appeared regularly in television dramas since, including the series "In the Heat of the Night," "Hannah Montana," and "All of Us," according to his profile on the International Movie Database.
Most recently, he appeared in two episodes of Criminal Minds. The last one ran in January this year.
During the run of "Designing Women," Taylor's co-star Dixie Carter described him as "a good man who is confident and strong. He's absolutely grounded," according to a profile in People.
"The eldest of three children of two former college professors, Taylor, a precocious child, first learned acting technique as a survival skill. 'The kids called me the Professor, and I got beat up a lot,' he says. 'So I dummied up until I got into the 11th grade,'" the profile read.
"Even when he didn't have any money, he always had style. He was on the cutting edge of men's colognes, and he was always buying yachting magazines and GQ," actor Joe Mantegna told the magazine.
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