Firstly, I dip a nylon brush into solvent and give the bore a few swipes. I then just rip off appropriate sizes of paper towel so as to fit snugly in the bore, soak them with solvent and run them through until they come out relatively clean. After the cleaning is done, another snug fitting piece with a little rust preservative on it will remove most of the residue and still leave a light film of preservative on the bore.
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