Before he picked up a pen and a microphone, Eliot picked up a blocker and goalie stick. The Hamilton, Ontario born Eliot played four years of college at Cornell University, the same school goaltending legend Ken Dryden attended. Though he graduated with a degree in agricultural economics, Eliot would earn a living in hockey.
Eliot was drafted by the Los Angeles Kings in the 6th round of the 1980 entry draft. The Kings were very patient with him, allowing him to complete his schooling and then allowing him to join the Canadian national team for the 1984 season and Olympics. Though he played backup to Mario Gosselin, Eliot appeared in 2 Olympic contests, one of the highlights of his hockey career.
Eliot jumped right to the National Hockey League the following season. He lost his first NHL game in overtime against Vancouver, but finished the season with a respectable 12-11-6 record. His goal against average was 4.37, high even in the high scoring era of 1980s hockey.
Eliot would struggle for ice time with the lowly Kings. Playing behind Bob Janecyk and Rollie Melanson, Eliot would appear in 51 games over the next two years. He would win only 13 of them.
Eliot was released by the Kings following the 1986-87 season, allowing the Detroit Red Wings to sign the goalie. He would serve as a depth goalie, seeing most of the season in the minors. He did appear in 3 games in a Wings jersey.
The story would be the same for what proved to be Eliot's final season in hockey as an active player. The Buffalo Sabres signed Eliot for the 1988-89 season. Though he got into two contests with the Sabres, Eliot was completely buried in the Sabres system. Darren Puppa, Jacques Cloutier, Tom Barrasso, Clint Malarchuk and Darcy Wakaluk were all ahead of Eliot. This prompted Eliot to retire.