"Tick-Tock Sick" is a song by Jim Henson released on a 45 rpm single in 1960, backed with "The Countryside". In what appears to be a joke credit (not uncommon for novelty recordings at the time), the conducting of the "orchestra" (only about three musicians perform) is attributed to Frank Sinatra.
The 45 record was recorded under the Signature label ("A product of Hanover-Signature Record Corp."). The main song was called "Tick-Tock Sick" and the flip side had a song called "The Countryside". Both were written by Jim himself. At the time Jim made the recording, he was living in Washington, DC and performing Sam and Friends on local television as well as making appearances on variety shows and making commercials for various products. It is not clear that "Tick-Tock Sick" was used for anything in particular, but it sounds like it may have accompanied puppet performances on Sam and Friends or a variety show. The theme of the song, the relentlessness of time, was later explored by Jim in his 1964 short film, Time Piece, and touched on again with the thirteen hour clock in Labyrinth.
Jim Henson accomplished an amazing amount in his life, but given the large number of files on unrealized projects that are in the archives, he clearly didn't have enough time to do all that he wanted to do. And "Tick-Tock Sick" tells us that he was already feeling the crunch just six years into his career.