"Horn broke(n)—watch for finger” has been a popular bumper sticker slogan since at least 1995. The authorship of the humorous saying is unknown.
While “giving people the finger” is certainly not unique to New York City, it is part of city lore. New York Governor Nelson Rockefeller (1908-1979) famously gave the Rockefinger/Rockefeller Salute to hecklers in 1976.
Wikipedia: Finger (gesture)
Linguist Jesse Sheidlower traces the gesture’s development in the United States to the 1890s. According to anthropologist Desmond Morris, the gesture probably came to the United States via Italian immigrants. The first documented appearance of the finger in the United States was in 1886 when Old Hoss Radbourn, a baseball pitcher for the Boston Beaneaters, was photographed giving it to a member of the rival New York Giants.
14 November 1995, Northwest Florida Daily News (FL), Bill Campbell column, pg. 1B, col. 1:
We’ll close on a lighter note, thanks to a bumper sticker seen by a reader: “Horn Broken. Watch for Finger.”
The Million-Dollar Tattoo
By Earl W. Emerson
New York, NY: Ballantine Books
There was a motto on the license holder: HORN BROKE—WATCH FOR FINGER.
University at Buffalo (NY)
Date: Thu, 10 Oct 1996 21:10:15 -0400 (EDT)
From: DragonTear Humor List
Horn Broken. Watch for Finger.
Mountain Bike! Florida:
A Guide to the Classic Trails
By Steve Jones
Birmingham, AL: Menasha Ridge Press
I knew I had to drive by a new set of rules when I began seeing bumper stickers like “Horn Broke— Watch For Finger” and “Keep Honking— I’m Reloading!” inside the back windows of cars.
Porsche Club of America
Bumper sticker - “Horn broke, watch for finger”
Napalm & Silly Putty
By George Carlin
New York, NY: Hyperion
Actual bumper sticker: HORN BROKE—WATCH FOR FINGER
The 2,548 Wittiest Things Anybody Ever Said
By Robert Byrne
New York, NY: Touchstone (Simon & Schuster)
HORN DOESN’T WORK. WATCH FOR FINGER. —Bumper sticker