Many rifles back then were left "in the white", and over a few months/years aquired the brownish patina you are looking for, the result of surface rust wiped and oiled repeatedly until it is evenly colored because there is no more clean metal to rust. Very attractive, and that layer of rust actually protects the steel from further rust, kinda like bluing does.
Enter modern science. People trying to replicate the look and feel of authentic early 19th Century muzzleloaders need something to duplicate the look of old guns. Slight sidetrack: Rust bluing requires the use of chemicals that will give an even layer of surface rust, then you boil the metal to convert FeO2 (reddish-brown rust, ferrous oxide) to FeO1 (black iron oxide, ferric oxide). Repeat the treatment as necessary until there is no more exposed iron/steel to rust, and you're done. Effective, but very time-consuming and tedious, and requires some special ingredients. Neat find: you could just rust the steel and not boil it, and it would be browned, like old steel barrels. Or, like many did, you could bury the steel in your back yard for a while and retrieve it when you thought it was done. Not very controllable, but effective. There was also ammonia pickling, fuming sulfuric acid, perchlorate, and a variety of other compounds that would rust the barrel and allow the same look as patina.
Enter more modern science. As caustic bluing becomes more common, unavoidably someone scratched their blue job. Now they need something to "touch it up". Easily done, if you are a chemist. People are happy once more. And now the muzzleloaders want something, too! You can make the same type of compound as cold blue, but instead of it turning black, it turns dark brown. Works OK, looks OK. Voila! Fait accompli!
And that is pretty much what BC Plum Brown is, a cold "rust"-coloring process for steel. Does it work? No doubt. Does it look good? Pretty good, sure. Does it look authentic? Weeellllll, maybe.