Eliot has been performing and teaching guitar and banjo since the fifties. In the ealy sixities he was director of the Philadelphia Folk Workshop, one of the county's earliest folk music schools. The staff performed as a bluegrass band.
In the late sixites he led the Great Metropolitan Steam Band which played ragtime and blues and recorded for the Decca label.
In the seveties he helped organize the Simcha Orchestra, one of the first of the West Coast bands reviving traditional Jewish Music.
Since the eighties he has led the Spirit of '29 Dixieland Jazz Band.
Since 2003 he has led Reinhardt Swing, a Hot Club of France style band.
As a single act Eliot plays and sings ragtime music. Also he does participatory music programs in nursing homes and senior centers.