Green’s Dictionary of Slang

(US) evening dress.

1909		Van Loan ‘The Low Brow’ in Big League (2004) 19: I want some of them – moonlight clothes [...] One of them open-faced coats that hangs down behind. [...] Ain’t I got any right to wear them moonlights?
1913		Van Loan ‘The Bachelor Benedict’ in Lucky Seventh (2004) 225: ‘The missus wants you to dress up in the clawhammer tonight. We’ll make it a regular function.’ [...] ‘Sure, Mace. I’ll put on my moonlights.’.