Green’s Dictionary of Slang

(US) a rest period between two shifts.

[1911		A. Adams Wells Brothers 🌐 Ch. ii: Those in the lead were point men, those in the middle were swing men, and the one who brought up the rear was the drag man].
1917		D.C. Roper US Post Office 353: Swing, period of time within the day’s tour or ‘trick’ when an employee is temporarily off duty. Swing room. Room where employees may spend their time while ‘swinging’.
1945		Transit News (Capital Transit Co., Washington, D.C.) 15 June n.p.: A ‘Swing’ works during the morning rush hour, and the operator is then off until time to start the evening rush hour [OED].
1972		J. Mills Report to Commissioner 129: I went on my swing after that [OED].
1987		M. McAlary Buddy Boys 31: [W]ondering why he had ever agreed to spend the first day of his three-day swing hanging foil wallpaper.
2017		R. Friedman Street Warrior 133: My off-duty time was becoming more important to me. [...] My swing—a cop’s version of a weekend, no matter what days it fell on—was time I could slow down.