I found a few things that might be of interest. The following quotes are from George Frederick Augustus Ruxton's Adventures in Mexico and the Rocky Mountains, Vol.II. London: John Murray, 1847:
At one point, Ruxton noted that he was in “…my camp, where I was very busily engaged in cleaning my arms” (p.111)
His travels were during the Mexican War, and he passed through an encampment of American volunteers: “Scattered about were tents and shanties of logs and branches of every conceivable form, round which lounged wild-looking Missourians, some cooking at the camp-fires, some cleaning their rifles or firing at targets…” (p. 175)
Ruxton was thrown from his horse during a river crossing, and dropped his double-barreled rifle into the water. It took him a little time to recover it .“As soon as I had secured the animals I endeavoured to get my rifle into shooting order, but the water had so thoroughly penetrated and swelled the patching round the balls, that it was a long time before I succeeded in cleaning one barrel, the other defying all my attempts. This was a serious accident…” (p. 264)
He was eventually able to clear the "stuck ball": “One evening a wolf came into camp as I was cleaning my rifle, one barrel of which was still unserviceable, and a long hickory wiping-stick in it at the time. As I was hidden by a tree, the wolf approached the fire within a few feet, and was soon tugging away at an apishamore or saddle-cloth of buffalo calfskin which lay on the ground. Without dreaming that the rifle would go off, I put a cap on the useless barrel, and, holding it across my knee in a line with the wolf, snap – ph-i-zz – bang – went the charge of damp powder, much to my astonishment, igniting the stick which remained in the barrel, and driving it like a fiery comet against the ribs of the beast, who, yelling with pain, darted into the prairie at the top of his speed, his singed hair smoking as he ran.” (p. 265)
After he crossed the border into the States, Ruxton met a number of Rocky Mountain trappers and hunters. He provided very detailed descriptions of their gear, appearance, and activities, including this: “Round the blazing fire the hunters congregate at night, and whilst cleaning their rifles, making or mending mocassins [sic], or running bullets, spin long yarns of their hunting exploits, &c.” (p. 282)
The quotes from Ruxton suggest that keeping guns clean was an important activity, although he didn't tell us exactly how it was done. However, I have a copy (facsimile reprint) of the Rules for the Management and Cleaning of the Musket, Model 1855. The original book was printed in 1862. There is quite a lot in it about cleaning and I'm not going to re-write every word, but a couple of things are worth quoting, as I expect the cleaning process used by civilians with their muzzleloading sporting arms would have been similar. One comment from the manual was "After firing, the barrel should always be washed as soon as practicable..." (p. 23). There are directions for removing the lock and dismounting the barrel for thorough cleaning, after which the soldier is directed to "...stop the hole in the cone with a peg of soft wood... pour a gill [pronounced "jill," equal to four ounces or half a cup] of water (warm, if it can be had) into the muzzle; let it stand a short time, to soften the deposit of the powder; put a plug of soft wood into the muzzle, and shake the water up and down the barrel well; pour this out and repeat the washing until the water comes out clear; take the peg from the cone, and stand the barrel, muzzle downwards, to drain for a few moments." The soldier is then directed to screw the wiper (worm) onto his ramrod and use a piece of dry cloth or tow to dry the bore, "...changing or drying the cloth two or three times." This is followed by an oiled rag on the wiper. The exterior of the barrel and the lock are to be then cleaned with a damp cloth followed by a dry one, and then an oiled one. I thought it was noteworthy that the book specifically stated not to remove the cone (nipple) or the cone-seat screw, which most of us now call the "cleanout screw."
As noted previously, Frank Mayer, the old buffalo hunter, gave a pretty good description of cleaning his Sharps. This was a breechloader, but he was shooting black powder: “We had some wild and wooly ideas about how to clean our rifles, I remember. We first drenched them with cold water, succeeded by a dosage of urine, which was well shaken up and allowed to circumnavigate the bore. I suppose the slight ammonical content of this homely but efficient solvent did the trick. We followed this with a thorough drenching of hot water, and wiped the bore dry and finished it off with a rag saturated with graphited tallow. If not cleaned before firing, the rifle shot a few inches higher for the first shot. We generally wiped out clean before firing; cartridges were too expensive to take any chances.” (Mayer, Frank. 1958. The Buffalo Harvest. Edited by Charles B. Roth. 1995 Reprint by Pioneer Press: Union City, TN, pp. 41-42).
I'm sure there are more primary references to gun cleaning out there, but just from these three we can learn a lot.
Best regards,
Notchy Bob