In the wake of John’s explorations, here’s another photographic perspective on the mystery building, looming in the left background with its distinctive cupola.
The view looks northeast from the southern tip of Marye’s Heights in May 1864. This detail is from an original image credited to the National Archives, and published in the Fredericksburg volume of Time-Life Books’ Voices of the Civil War series.
I’ve included in the detail the roof and upper story of the brick Stratton House, which stood and still stands a short distance in front of the famous stone wall, at lower-left corner for orientation.
(Unfortunately, a better resolution of the Archives photo is not readily available at present, while a print of the same view, posted online at the Library of Congress’ Prints & Photographs website, appears to offer even less resolution.)