Career
In 1925 the pair moved on to Los Angeles, eventually forming the Rhythm Boys trio with singer/songwriter/pianist Harry Barris. Barris wrote the songs Mississippi Mud, I Surrender, Dear, and Wrap Your Troubles in Dreams among others. The singing group worked with Paul Whiteman's Big Band for three years.
They went out on their own for a year until Crosby effectively dissolved the group to go solo. The Rhythm Boys were filmed for the Paul Whiteman movie The King of Jazz (1930) singing Mississippi Mud, So the Bluebirds and the Blackbirds Got Together, A Bench in the Park, and Happy Feet. According to a filmed interview of Rinker, Crosby performed the first two weeks on his first film while on daytime work release from jail after crashing his car into a telephone pole while driving drunk.
After the Rhythm Boys broke up, they reunited only once, to appear together on the "Paul Whiteman Presents" radio broadcast on July 4, 1943. In 1952, a song for which Rinker wrote the music with lyrics by Floyd Huddleston, You Can't Do Wrong Doin' Right, appeared in the film Push-Button Kitty and in the television series The Many Loves of Dobie Gillis. He also wrote the song Ev'rybody Wants to Be a Cat also with Floyd Huddleston for the Disney animated children's movie The AristoCats (1970).
It was a musical family: his father, Charles, played fiddle and called square dances and his mother played piano every evening after supper. Rinker married Elizabeth Neuberger on October 25, 1938. She became the first woman to join a band as a full-time singer, as Crosby had been the first man to do so.