When I first started working for Green River Forge, we used the Plumb Brown and I've used this same procedure with any brown I use. During the browning, I have already placed a tapered dowel pounded into the muzzle and then before washing, a round splinter in the touch hole. Because Plum Brown is a very shallow brown and light, just rinse off with a soft tooth brush to get rid of the loose chemical residues. Be careful of any fine steel wool for the rough spots, but regular use of steel wool usually applies to other types of browning. Next, a very light scrubbing with baking soda that has water mixed to a soup stage but not too runny. It has to partially stay in place to do it's job, just like when you clean battery terminals on your vehicle. Rinse that off with running water and the brush. When all the residue is gone and you have wiped everything down, you need to get rid of the moisture out of the steel. Moisture, no matter how well you oil, the moisture is still underneath and will still cause rust to reappear if you don't get rid of it. Clamp the barrel in a vice or whatever you choose to use and take a torch to the barrel, but not dead close or Mr Scorch will attack. Move the flame around the barrel and watch for the moisture line moving away from the flame ahead of you. spend a little extra time with the tenons and breech plug area so you make the water sizzle out of the crevices. Probably about half way through, with the barrel still hot/warm, liberally apply high carnauba wax content wax like Meguires to the barrel with a rag. watch it melt into the creviceWhile it is getting cold, apply more to keep a coat on it until cold. Let it rest for a few and buff it out. You may get some rust the next day, so you card off with fine steel wool so you don't wear the high spots and then you torch it up again so it is warm. It may catch fire, so what. Add more wax.. Let it go stone cold and buff out again. Keep waxed through it's life. If you use oil, the oil will transfer to you and everything else and that's yechy. Well, you get the idea, I may have muddled some of the narrative, but you get the idea to polish the details yourself.