The Brits did leave the odd weapon here 1812 - 1815
In my remarkably foolish youth I owned a converted India pattern musket, purchased on the Eastern Shore (Delmarva Penninsula) The Brits had been pretty active in the Chesapeake Bay.
Still have a flint Paget carbine, bought from a man who collected it in North, i believe, Carolina, 1941 from an old house. Maybe the Brits let it there, or maybe it came through the Port of Wilmington, NC, on a blockade runner. Early in the Misery between the States some Southern cavalry, so it said in an old Civil War times, preferred flint carbines. Don't have to fiddle with a cap. Personally I find caps a @!*% nuisance, so sympathize.
Do you know any family history, like where did they live 1812-15??? Family stories can be squirrely, but some people do have long memories. Grandfather was still a bit angry when he told me how the Brits stood one of my uncles in lime water, in the hold of a British prison ship. I read part of that man's pension application and can only imagine what stories were handed down in earlier generations.
Might not an officer carry his own arms? Hence Ketland? Simple construction to fit the officer's budget.
