Like 25+ years ago I made a damp box with couple a small blocks of wood to sit the barrel on, while I apply the browning solution. First to raise the humidity in the box , put some small water soaked pieces of wet rag in the box , but not touching the metal to be browned. Before starting , put on a pair of the cheap clean brown cotton gloves. Any time you touch the metal , make sure your gloves are on. Have used several kinds of browning solution , and found Laurel Mtn. Forge ,ok. Davis' is ok, can't remember some of the others , just not B.C. Plumb Brown . I prefer a finely brushed finish in my browning jobs , so once the draw filing , emery cloth work is done, I use a very fine wire wheel on the metal. The wire wheel degreases the metal , so that eliminates any need to use chemicals that could ruin the finish. The most important trick , is to use a damp , not sloppy dripping , 3/4" across , by 1/4 "or around that size , thick clean tee shirt material piece of rag with shredded cloth bits to come from it while applying the browning compound. When you apply the browning compound , wring out the applicator a little and begin brushing the solution on with NO runs , and no puddles , and minimal solution on the metal. Don't touch the wet browning solution on the metal and close the lid on the box. This method is quick , if done properly , one app. should do it in 12 hours. , Two , will darken the brown , but the metal might need carded. When the surface and color are acceptable, wash the barrel under a faucet , dry the metal with a heat gun or a torch hot to the touch , and apply a rust inhibitor like gun stock finish ,or boiled linseed oil and wipe down with a cloth until dry. A coat or two of paste furniture wax is last. I also don't brown the wood side of the barrel but make sure the barrel channel has finish on it...................oldwood
