The Galactic Plane was searched for transient, monochromatic light at optical and near-IR wavelengths to detect pulses shorter than 1 sec. An objective-prism Schmidt telescope of 0.28-meter aperture and a CMOS camera were used to observe 973 square degrees, with 8864 exposures of 1-sec each, within a strip 2.1 deg wide along the Galactic Plane, from Galactic longitude -4 deg to +248 deg. All exposures were analyzed for transient, monochromatic sources using a “difference image” algorithm that yielded 11 candidate sources. All 11 sources were found to be associated with either astrophysical emission-line objects or aircraft with sub-second blinking lights. Our survey “rediscovered” many Wolf-Rayet stars, M dwarf flare stars, and planetary nebulae. It also identified an aircraft, of unknown type, that apparently had a nearly monochromatic lamp and a xenon lamp. This survey would have revealed optical and near-IR pulses having a power of ∼180 GW (wavelength dependent) if emitted by a 10-meter aperture laser located 1 kiloparsec away. These non-detections of laser pulses from the Galactic Plane, including a 10-degree region toward the Galactic Centre, add to the non-detections from more than 5000 nearby stars. Indeed, all-sky surveys for emission-line objects (e.g., ionized gas, supernovae remnants, and active galactic nuclei) would have revealed lasers of a wide range of average brightness, wavelength, and cadence. The absence of beacons reveals more of a SETI desert, notably at the intensely surveyed optical and radio wavelengths.