The Gomez House is a reconstructed example of a First Spanish Period (1565-1763) structure. This structure was built of board-and-batten, an unusual construction material in Spanish St. Augustine. The home was occupied by infantryman Lorenzo Gomez and his family, who departed St. Augustine for Cuba in 1763. The home was demolished during the British Period (1764-1784). It was reconstructed by the State of Florida in 1969.
The full Wikipedia entry for the Gomez House is available here.
The block and lot location of the Gomez House is Block 7, Lot 2 (B7L2)