IMHO ...
i will preface to say that in all NORMAL circumstances, all that's ever needed to clean out black powder fouling is plain ol' tepid tap water. anything else is a waste of money and perhaps time.
pull the lock and stick it in a bucket of tepid tap water, to be revisited when the barrel's cleaned and oiled.
if the barrel is pinned, plug the touch hole with a round toothpick, pour fill the barrel with the tepid water and let it stand for 2 to 5 minutes - allow the water to do its job. turn the touch hole so it's facing the ground and pull out the toothpick and for flat breech plugs, use a scrapper clean off the plug's face. if a patent breech, after using the scraper, run a .22 bronze brush wrapped in a wet patch down into the breech's flue to clean that out. then finish up by plunging a water wet patched jag up and down the bore 'til the water pissing out the touch hole is clean. run down dry patches and then one oily patch - almost ANY oil will do just fine, don't waste money on fancy expensive stuff. there is no need for special "bore cleaners" or "bore oils" or added cleaning steps.
if the barrel has a hook breech (yer hawken type rifles), pop the barrel wedges, lift out the barrel, set the ignition end in a bucket of tepid tap water and plunge the bore with a patched jag. when the water pisses out clean, see above.
now attend to the lock - use a toothbrush to clean while the lock's in the bucket of water. when cleaned out, paper towel pat dry well, use wd-40 spray or an oily rag to coat all the lock parts and the complete lock plate. paper towel pat off any excess oil. put the lock back.
done.
HOWEVER, pitting is a total 'nother story and that must be resolved first and foremost. posts here address what needs to be done to rid of pitting and restore the barrel to the point that the NORMAL cleaning process can be administered effectively.
