There are actually 2 ways to clean between shots.
1. load and fire your first shot. Snap a cap to make certain the flame channel is clear [optional], Add powder, wad, Clean down to the wad....two DAMP patches followed by 2 dry patches, add bullet of choice. Fire. DO NOT have your cleaning patches drippy wet! Excess liquid will run out of the patch into the patent breech and wet the powder charge and cause a misfire.
2. Fire the shot, clean.....2 damp, 2 dry patches, CAUTION...this way may push fouling into the patent breech causing a misfire if you dont snap a cap to clear flame channel, add powder, wad if desired, bullet of choice, fire. Just so you know, the Gibbs has a patent breech. You will need to wrap a patch around a .22 cal. brush to clean it. Remove nipple, clean it. Bend a pipe cleaner into a "J" shape to clean the flame path from the nipple hole into the patent breech. I was never a fan of submerging the breech end of the barrel into a tub of water and pumping water in and out. I use windshield washer solvent to clean at the end of the day followed by patches wet with 90% isopropyl alcohol to mix with and evaporate any dampness left in the barrel. Dry patches followed by coating the bore with "rig".
Generally in my experience, if you get a misfire, you can trace it back to improper cleaning of the patent breech/flame channel.
The mixture I use on my patches to clean between shots is ready to use antifreeze but any mixture that contains water will work just as well. Water with a little Dawn dish soap is simple and works.
There is a small learning curve to find out what works for you but that is all part of the fun. As you have seen, there are several Gibbs owners in the group so info wont be hard to get. Have fun on your journey! X