Eliot was born in Milton, Ontario. He graduated from Cornell University in 1983 with a degree in agricultural economics, having been elected to the Sphinx Head Society during his Senior year. He earned membership into the Red Key Society for students exemplifying excellence in academics and athletics. With the Cornell Big Red men's ice hockey team, he was a two-time All-Ivy selection and was named an All-American as a senior. He was inducted into the Cornell Athletic Hall of Fame in 1996.
On September 12, 2014, it was announced that Eliot was named the new Director of Minor Hockey Operations for Little Caesars Amateur Hockey. In his new role, Eliot will oversee the day-to-day operations of the Little Caesars AAA hockey program and the Little Caesars Amateur Hockey League (LCAHL), along with serving as the organization's representative to USA Hockey, the Michigan Amateur Hockey Association (MAHA) and the High Performance Hockey League (HPHL).
Eliot currently works as an in-studio analyst for Fox Sports Detroit's coverage of the Detroit Red Wings. He also contributes as an online columnist for Sports Illustrated. Previously, he worked as a national color analyst for Versus as well as locally for the Atlanta Thrashers telecasts on Fox Sports South and SportSouth. He also does occasional work for the Big Ten Network.