Green’s Dictionary of Slang

1. a squint or the eye that has it.

1837		Kentish Gaz. 11 July 3/4: He of the ’swivel-eye’ is woundily annoyed at his friends having found occasion to laugh at him.
1840		Freeman’s Jrnl (Dublin) 22 Jan. 3/3: The defendant, tall, boney, gaunt and grim, with a swivel-eye adapted to see round a corner.
1849		Leamington Spa Courier 5 Apr. 3/7: I don’t know the names of the lodgers — one we called thomas, and the other was a swivel-eyed man; we used to call him ‘swivel-eye’.
1865		Dickens Our Mutual Friend (1994) 351: She found herself possessed of what is colloquially termed a swivel-eye.
1867		Huddersfield Chron. 13 Apr. 3/1: I ’ad a aunt myself as squinted that wiolent as could see the back of ’er ’ead, and Mrs Partis ’ad a swivel-eye ’erself.
1874		Peterborough Advertiser 28 Nov. 4/4: A queer-looking man with a swivel eye.
1883		Bell’s Life in London 5 May 3/5: A man with a ‘swivel eye’ is [...] awkward to deal with. You have an uncomfortable feeling [...] that he is somehow or other ‘running the rule’ over you [...] with the moveable orb, while he is preparing to back up a good fat lie with the stationary one.
1895		Sth Wales Dly News 30 Oct. 4/2: The anti-Pumpist [...] changed the issue by insinuating that the Pump advocate’s sister had a swivel eye.
1915		Rochdale Obs. 16 Jan. 2/3: The left eye was a swivel eye and served the purpose of preventing one from determining which one was gazing at you.
1924		Evesham Standard 29 Mar. 2/2: The left eye was a swivel eye.
1936		R.F. Adams Cowboy Lingo 179: We call to mind many seemingly mysterious monikers, yet each peculiarly fitted the individual [...] Bug-Eye, Swivel-Eye.
1941		Baltimore Sun (MD) 11 Aug. 4/6: ‘Dolfuss.’ ‘The swine,’ roared Swivel-Eye.
1999		Boston Globe (MA) 30 June 23/3: A Lutheran lawyer with a flytrap mouth [...] A lecherous broker with a swivel eye.

2. a swindler, a term of abuse.

1891

A. Day Mysterious Beggar 334: ‘Workin’ it down,’ be ye, y’ ole swivel eye!