Stucker was born in Des Moines, Iowa. His family moved to Shaker Heights, Ohio, where he distinguished himself in school as a pianist and class clown.

He graduated from high school in 1965. Stucker made his screen debut co-starring in the 1975 comedic sexploitation film Carnal Madness as Bruce Wilson, a gay fashion designer who escapes from an insane asylum with two fellow inmates, fleeing to an all-girls school. He went on to perform in the 1977 earthquake-in-Los-Angeles comedy Cracking Up, alongside Fred Willard, Michael McKean, and Harry Shearer.