The Turtlenecks was a band in which John Flansburgh performed briefly. A sample of the type of music that they made can be heard on "Indiana Wants Me". According to the TMBG Unlimited description of that song, the band included Karl Hecksher (drums), Julie Kantner (bass), and Fred Hickler. The Turtlenecks also featured Chris Lawrence of Annabouboula, who was John Linnell's roommate in 1984.
From an interview with Flansburgh:
Then I had this band that was the immediate predecessor to They Might Be Giants in the sense that, I feel the spirit of the band was more kind of coming from where They Might Be Giants was coming from. It was a group called The Turtlenecks. We did all original material...uh, except 'Sweet Home Alabama.' The bass player could play the entire riff on the guitar, so it was like...this impressive display...So we were called The Turtlenecks, we played a bunch of songs...and the drummer of the band had this weird thing. He liked stopping in the middle of songs, and waiting 'til everybody would turn around...and just as the thread of the song was about lost, he'd start playing again. So, like, we wouldn't actually stop playing, but he would stop long enough to make everybody feel really edgy. And he'd do this in performance, at shows! It was really this strange control thing, he was trying to show that he was driving the car. So that was the group; we actually did a couple of songs that are still in our repertoire. 'Alienation's For The Rich' was written for that band.