Even after the lighthouse was completed, it was not lit for another two years, first shining out of its distinctive two windows on September 7, 1792.
At the time of this map, Alexander Hood Cocken was keeper on McNutt's Island. He had taken over lighthouse duties after the death of his father Alexander Cocken, the first keeper, in 1812.
I found this map in W.O. Raymond, "Colonel McNutt and the Pre-Loyalist Settlements of Nova Scotia," Transactions of the Royal Society of Canada, 3rd series, vol.V, 1911, sec.II, 23-115, p.97. The map and article can be found online at www.archive.org.