The identity of a soldier in an unknown soldier grave on Route 5 in Caledonia, Livingston County, New York, is actually not a mystery. As noted at FindAGrave:
Although officially an "Unknown Soldier", this is generally believed to be the burial site of one Private John Alexander, murdered by a fellow soldier, Private William Comfit. The site is believed to be the encampment site of a troop of American soldiers on their way from Buffalo to Sackett's Harbor.
A poem put to song, "The Faded Coat of Blue," was appropriate for the Civil War era, but was written as a tribute to Livingston County's unknown soldier. Four verses of the poem, written by a Caledonia poet, is inscribed on the grave marker.
However, there is a mystery surrounding the grave. As noted in a newspaper article, it's the mystery of a plant growing on the grave.
The flower, called the Blue Gentian, is said to be commonly found in areas where soldiers’ bodies are buried, and only along the Atlantic coast. The Blue Gentian no longer blooms at the gravesite, but the story still intrigues all those who read of it. [Source]