Green’s Dictionary of Slang

1. a police officer [SE blue lights on police cars + play on blue-plate special].

1994		G. Smitherman Black Talk.
1999		Falls, Off the Rocker 1 Oct. 🌐 She then told me about one police officer who used to remove the light beacons from the top of his patrol car and make them a part of his Friday night cross-dressing party outfit. He was known in cross-dressing cop circles as ‘Everybody’s Blue Light Special’.

2. a cheap, low-quality retail item.

1997

Simon & Burns Corner (1998) 65: The touts are constantly trumpeting blue-light specials: two for the price of one, or a free vial of coke for every dime of dope.