Elliot was born in the Scottish Highlands, but moved to Los Angeles, California with his family at the age of three.

Elliot started out as a member of the jazz-rock unit, KittyHawk, playing lyricon (a wind synthesizer) and saxophone, and recording several albums with them.

He then became a member of the funk band Tower of Power, playing tenor sax for five years during the 1980s.

Elliot participated with fellow saxophonists Paul Taylor and Gerald Albright, as well as keyboardist Jeff Lorber, in the "Grooving for Grover" concert series.

The series honored the legacy of the late Grover Washington Jr. Elliot was known for his zebra-striped tenor saxophone.