I do the same thing with T/C #13.I usually reserve these patches until I am done and run one or two down the bore to get it somewhat clean and keep the remaining fouling soft until I get home.
But normally whether I am shooting Pyrodex or BP, I put a cotton patch in my cheek before I load my rifle and fire it. After shooting the charge, I remove the patch and it is usually just damp so I swab the bore, both sides of the patch, then a dry patch. Put another patch in my cheek and start all over. This usually get the bore pretty clean.