Dąbrowski has an unidentified “American Masonic Symbols”, see below top left. It appears to (sometimes) be an emblem of an officer in Templar degrees (see below top right).
In the 1862 The Freemason’s Manual of Jeremiah How, there is a more modern Templar tracing board which has a cock on the bottom left of the triangle (see below, bottom left).
The cock is also a somewhat common element of (European) rooms for preparing the candidate (bottom right).
Top and top left: Dąbrowski P. 180. Year and designer unknown
Top right: The Templar’s Chart of Hieroglyphic Monitor by Jeremy L. Cross (1821)
Bottom left: The Freemason’s Manual by Jeremiah How (1862)
Bottom right: Maçonnerie des Hommes 1766