It has been perched for ages atop the city’s swarm of yellow taxis, an illuminated language in which it seemed only New Yorkers were fluent.

The off-duty light means off-duty, but only sometimes. If the light says a driver is both available and off-duty, a passenger’s desired destination is often the tiebreaker. Everything is negotiable.

“Sometimes,” said Marvin Taylor, 36, a court stenographer who claims to have spent much of his young adulthood cajoling drivers to Park Slope, Brooklyn, “you’ve got to use the gift of gab.”

Soon, though, that gift may be of little use. The city’s Taxi and Limousine Commission voted Thursday to overhaul the roof-light system for yellow taxis, eliminating the off-duty designation so that the lights will convey only two possibilities: available or unavailable.