At two hours before midnight on October 11, Columbus saw a dim light "like a little wax candle, rising and falling." He mentioned this to at least two others aboard the Santa Maria, Pero Guiterrez and Rodrigo Sanchez de Segovia. Guiterrez also saw the light, but Sanchez did not. The light was seen once or twice more, but then was not seen again. According to later testimony in a lawsuit, the light was also seen aboard the Pinta at about the same time.
The actual landfall island was seen four hours later (at 2 a.m. on the 12th) at a distance of 2 leagues. The fleet was sailing west at 12 miles per hour that night (8 knots in modern terms), so they must have been between 32 and 37 nautical miles east of the landfall island when the light was seen.
The problem here is that you can't see a low Bahamian island from these distances. Morison suggested that Columbus's eyes were playing tricks on him, which sounds reasonable until we recall that the light was seen by perhaps three people on two different ships.
In 1959, Ruth Wolper organized an experiment in which she set a giant bonfire at High Cay (an islet off the coast of Watlings) and sailed east from the island until the bonfire's light was no longer visible. The last glimmer was lost at a distance of 29 nautical miles, significantly short of the requirement (although that did not deter Wolper from claiming success in her experiment). Wolper was able to see as far as she did only because of the phenomenon known as "looming": when a very bright light illuminates the air above, the air itself becomes visible even when the light source is below the horizon. It is unlikely in any case that the natives would have made a bonfire this large; and even if they had, it would have become more visible as the fleet approached, while Columbus lost sight of the light almost immediately.
Josiah Marvel, an advocate of the Grand Turk theory, has proposed that the light was caused by bioluminescent protozoa on the rocks of Mouchior Bank (located east of Grand Turk). But the light Columbus described -- like a little wax candle -- strongly suggests a point source. This would rule out both bioluminescence and looming effects.
Of course, some proposed landfalls have other islands to the east, which would have been bypassed in the night -- but which could provide a source for the light in the form of an Indian campfire or other habitation. Landfall theories with this advantage are given preference on this clue in the scorecard.
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