When I was young & even dumber than I am now, I bought an India pattern Brown Bess, converted to percussion, from a shop in Salisbury, Maryland. That is on the peninsula est of the Chesapeake Bay.
Had I been thinking, I would have realized that this was a left over from when the Brits sailed up that Bay during War of 1812, and I might have treated it more reverently. Instead I nailed on some castings to reconvert it, & sold it.
One thing I remember about that faded old stock finish. It had some manner of reddish-brown pigment on it.
Never have read what that might have been, other than the original finish of the time.
Otherwise i agree with whoever said he had (had seen?) old muskets with a shiny finish, not that dull finish later American muskets had from being cooked in linseed oil + (real) turpentine. I have both a long land - which is no longer long at all - and an India pattern w bayonet, that looks like it saw service.