[1] Goelz applied to work at Walt Disney Imagineering, but was not considered on the basis that they had sufficient industrial designers already employed.

[3] During this time, Goelz regularly viewed episodes of Sesame Street, fascinated with the design process behind the Muppet characters, costumes, and performances, leading him to wonder about the creators behind them.

One month later, following an invitation from Oz, Goelz attended daily tapings of Sesame Street during a work trip to Pennsylvania.

Eight months later, in the fall of 1974, Henson offered Goelz a full-time position as a designer and puppet builder, and occasional performer in specials, while allowing him to retain his main industrial clients.

[9] Returning to New York, Goelz began work on The Muppet Show: Sex and Violence, where he built the puppets Nigel, Animal, Floyd Pepper, and Zoot, the latter becoming his first major character.

The puppet previously debuted in The Great Santa Claus Switch as Cigar Box Frackle and had made brief appearances in the Muppet Meeting Films and Herb Alpert & the Tijuana Brass, with different performers.

Goelz recalled the hectic schedule of working full-time behind the scenes and in front of the cameras, describing his typical day as involving running back and forth between making puppets and performing.

[4][11] The early design of Gonzo featured a permanently sad expression, which influenced Goelz to give the character a similarly depressed demeanor.

Goelz described the character's downcast eyes as making him easier to play, reflecting his own feelings of being an impostor in show business and learning to perform and puppeteer on the job.

[14] In addition to the starring role of Gonzo, Goelz also performed saxophone player Zoot and scientist Dr. Bunsen Honeydew.

Goelz also performed Uncle Traveling Matt, Philo, and the World's Oldest Fraggle, as well as a variety of guests and incidental characters.

Goelz also worked on Henson's forays into the fantasy genre, performing skekUng and Fizzgig in The Dark Crystal and Sir Didymus in Labyrinth.

[11] Following Henson's death in 1990, and with Oz focusing more on directing, Goelz's role as Gonzo gained increased prominence, beginning with The Muppet Christmas Carol.

[5] Over the years, Goelz has sustained a number of injuries due to the physical positions Muppet performers must maintain for extended periods and contort into small spaces.