The mature fruit can be cut off the plant when the weight of the fruit causes them to fall over, as shown iby the two fruit on the left side of fliptop's photo. The two vertical ones on the right should be left for now, but they are not far behind.
As RS noted, leaving the fruits to ripen on the plant will invite unwanted guests. Fortunately most humans have no clue that these are edible, even here in Miami where they have been grown for 100+ years, so the critters are the big concern.
The scales of a mature fruit will start descaling after 5-7 days on average, starting at the basal end. As Carolyn mentioned, let the scales fall off (or pull back) naturally, otherwise the oxalic acid will cause the stinging sensation. It is bad enough on your tongue, but if it hits your throat, it can be much worse.
The paper bag works well if you want to have more, or even all, of the fruit to ripen at the same time. This is the result of the fruit's naturally released ethylene gas levels being enhanced/trapped in the bag, so adding some banana or apple will speed it up even more.
Enjoy!