Two years of service in the United States Army interrupted his minor league career, but he was called up by the White Sox in 1970.

A member of their Opening Day roster in 1971, he posted a list of White Sox left-handers on his locker door, crossing names off each time he thought he had passed them on the depth chart.

[1][2] Elmer had once been a baseball player himself, pitching, catching, and playing the outfield in the St. Louis Cardinals system until he started serving in the United States Marine Corps during World War II.

The Chicago White Sox signed him in 1965 as an amateur free agent, though he was expected to attend college for a semester before joining the organization.

[5][6] Eddy made his professional debut as a pitcher in 1966 with the Deerfield Beach Sun Sox, which moved to Winter Haven, Florida, during the season.

[8] After the season, he pitched in the Florida Instructional League and also played winter ball in Venezuela with the goal of developing a better slider.

[3] He made his MLB debut on September 7, pitching an inning of scoreless relief in a 7–5 loss to the Oakland Athletics in the second game of a doubleheader at Comiskey Park.

After seeing him pitch in spring training, Chuck Tanner, the team's manager, said "Eddy can be our most dependable pitcher in short relief".

"It was a big joke in the clubhouse," recalled fellow left-hander Tommy John, who eventually saw his name crossed off the list.

[12][16] In 24 games (four starts) for Tucson, Eddy had a 3–2 record, one save, a 6.85 ERA, 41 strikeouts, 34 walks, and 57 hits allowed in 46 innings.

[5] Eddy was one of the last players cut from White Sox spring training in 1972, as he was reassigned to minor league camp on March 31.

[18] After starting the season at Tucson, he was sent to the San Diego Padres on July 16 as the player to be named later in an earlier trade for Ed Spiezio.

[1] He finished his MLB career with an 0–2 record, a 2.36 ERA, 23 strikeouts, 25 walks, and 29 hits allowed in 34+1⁄3 innings pitched over 29 games.

[3] Regis McAuley, sports editor for the Tucson Daily Citizen, thought Eddy was similar to Whitey Ford, both in stature as well as in his reliance on carefully thrown fastball.

[4] Eddy listed Ford among the left-handed pitchers he enjoyed watching on television growing up, along with Billy Pierce and Herb Score.