Green’s Dictionary of Slang

(Irish) to flirt.

1976		Wicklow People 16 July 7/3: Bird Talk [...] we acted the linnet and used a yellowhammer to attach flycatchers and bunting to a kite.
1987		L. Redmond Emerald Square 143: Sloppy Molly was nuts about her father’s new assistant. Nobody ever caught them acting the linnet or anything like that, but it was the very lack of any bit of flirting in public, that put them on to Molly.