He did not indicate where he had bought them, but it is very likely that they were in a sale of items belonging to a distressed French aristocrat. The King had fallen three months earlier, and would be guillotined two months later, and aristocrats had been forced to flee France or face imprisonment and possible execution. Morris bought quite a few pieces of furniture, beddings, curtains, etc. in these sales, and shipped them to his home in the Bronx. When he returned from Europe in December 1798, he started extensive renovations to the family mansion, which had suffered during the American revolutionary war. Morris had purchased the house and land from his oldest half-brother Staats Morris before he had left for Europe in 1788. He used his French aquisitions to furnish it in a grand style.
The table, with its lid open, showing the mirror, can be seen in this print of the Morrisania library, which appeared in an 1890 article in Art Journal about the Morrisania mansion. at the New-York Public Library:
The Miriam and Ira D. Wallach Division of Art, Prints and Photographs: Print Collection, The New York Public Library. "Gouverneur Morris" New York Public Library Digital Collections. Accessed July 5, 2022. https://digitalcollections.nypl.org/items/6b0efb70-cd39-9c8e-e040-e00a18065a96
The prints in the article also show the reception room and front hall of Morrisania, and several other items purchased by Morris (the large desk by the dressing table, a clock, etc.) are still known to be in existence.
It is thrilling to think that Morris probably looked at himself in that mirror.