Green’s Dictionary of Slang

gaga v.

[gaga adj. (2); + ? the ga-ga noises of babytalk]
(US)

1. to act sentimentally.

[US]I. Franklyn Knights of the Cockpit 120: I don’t care for that sort of ga-ga-ing!

2. to persuade, to ‘sweet talk’.

[US]S. Morgan Homeboy 23: The girl [...] whose charge it was to gaga, goose, or garotte incoming rubes into buying a drink.