Green’s Dictionary of Slang

swivel n.

a glance, a look at.

1914		Ade ‘The New Fable of the Father Who Jumped In’ in Ade’s Fables 87: In a crowd of Bank Directors he would have been a cheap Swivel, but among the Women Folks he was a regular Bright Eyes.
1938		D. Runyon ‘Big Shoulders’ in Runyon on Broadway (1954) 587: She is hoping she may get a swivel at Charlie.
1943		R.L. Bellem ‘Dead Man’s Shakedown’ in Dan Turner Detective Mar. 🌐 Evidently she’d come to cop a swivel at herself as of twelve years back.

SE in slang uses

In compounds

In phrases

on the swivel

active, showing one’s paces.

1889

‘’Arry in Parry’ in Punch 29 June in P. Marks (2006) 95: But when ’Arry is well on the swivel he makes Cairo donkey-boys stare.