[wogpotter]

I had exactly the same issue as you with a new BP rifle that had sat unassembled for 30 years. At first I supposed it was light non-pitting surface rust, reasonable assumption given the 30 year delay in being fired.

I cleaned with hot soapy water, rinsed with hot clean water & dyed with a hair dryer till it was bone dry. I then lubed the outside & inside generously with gun oil. (I'll remove the gun oil before firing & use a BP lube).

The brown stuff you describe reappeared. It seems to be an after effect of Pyrodex, rather than rusting bore metal as the bore is slick & smooth, but the brownish-red stuff reappears even through a layer of gun oil.

I say this because my other BP guns are treated in the same way & have zero red stuff, the difference is that they have never had Pyrodex in them.

Do oil thoroughly & clean well to prevent actual rust & bore damage, but look to other possibilities as well.