Saxophonist Charles Neville — forever known to fans as “Charlie, the horn man”—was the secret ingredient in the Neville Brothers’ mix, the brother whose jazz instincts took them to another level. Neville, who died last month of pancreatic cancer at age 79, was also a link to the fabled days of the Dew Drop Inn, where he began performing in the ’50s.

As the one Neville who didn’t si...