A running light was a source of illumination mounted on the exterior hull of a starship or other spaceship.
Starboard and port-side running lights were situated on the rim of the primary hull of refit Constitution-class starships. There was one each on the dorsal and ventral surface. (ST reference: Mr. Scott's Guide to the Enterprise)
In August of 2376, science officer Croth suggested using the USS Gryphon's running lights to tap out a message to the USS T'Kumbra, as his ship's communications array was damaged. (DS9 - Mission Gamma novel: Lesser Evil)
In January of 2384, Commander Worf saw the runabout USS Roanoke's running lights through fog as it landed nearby. (TNG - Cold Equations novel: The Persistence of Memory)