"Swivet" is a fun word. No source I've found has any clue of its origin, but all agree that it's an informal word, most commonly used in the phrase "in a swivet." The definition is a little vague: some kind of condition of excited distress or agitation: different definitions give synonyms as "in a snit," "in a state," "in a sweat," "in a tizzy," "in a huff." So a swivet can be an emotional state of anything from anger to anxiety.

There are also two other independent definitions of "swivet" which both come from combinations of separate words. In line/country dancing, a swivet is "a two count move where one foot does a pivot and the other foot does a swivel at the same time."

International Source for Ergonomics has apparently trademarked "swivet" as a name for a swivel-and-tilt (hence the name) surface for one to use a computer mouse on.

Worksurfaces.com and a few other electric/electronic work supply sites advertise a product described as a brass grounding swivet which rotates while maintaining a constant connection with ground to assure personnel protection, but I haven't found if this swivet comes from swivel and tilt, pivot, or some other source.

There also seems to be Swivet Records, which released "Life Religion & Love" by Thrill Deluxe, and Swivet Music, which is credited with Dann Gunn's "Floating, Spinning, Upside-Down" album.

http://education.yahoo.com/reference/dictionary/ entries/00/s0950000.html