Eidson attended Morgan County High School (now Hartselle), where he practiced football, golf, shot put and the discus throw.
Eidson was selected by the Dallas Cowboys in the second round (55th overall) of the 1976 NFL draft, with the intention of switching him to offensive guard.
As a rookie, he was a backup guard and center, playing in 9 games and was a part of the Super Bowl XII championship team.
In 1977, he suffered a jammed neck during a training camp blocking drill against defensive end Ed "Too Tall" Jones and experienced temporary paralysis.
Eidson went on to earn his MBA from Southern Methodist University's Cox School of Business and was elected to Beta Gamma Sigma academic honor society.