I use a wide variety of cleaning "tools"..( laughing here)
Mostly I use a toothbrush, to scrub stubborn carbon build up, after it's been moistened with Ed's Red, Hoppes #9, FP-10, even WD-40, whatever I happen to select. I use q-tips for cleaning tight spaces, where residue collects.I started using napkins/ paper towels instead of cloth, to wipe off residue & even as a patch
over a jag on on a brass brush..they're very absorbent & usually around my bench from the last food I've consumed.
I do have a seabag filled with old t-shirts ,flannel shirts, etc..that I sometimes use as patch / rag material.