Like Richdeer said. Wahkon Bay works good, it is a traditional rust browning (acid wear latex gloves).
Easier tahn building a box is just use a large plastic bag, that you blow up, you moist breath will but moistur in it, or some wet paper towels. BUT remember anything that touches the barrel, part will tend to change the color, meaning a light spot or a dark spot.
Best is to do one half end of the barrel and then when that dries do the other side over lapping remember you will be building coats, one a day for me. So one day do the middle of the barrel. You have to use your judgement to get it uniform. but you really don't want it perfect,if you want the 'original' look.