About pistols

Can anyone tell me when do the pistols start turning brown

Once they have reached that point of maturity. Its not a set time frame, every plant is different. The stigma(pistils) are one of the first signs that the plant is starting to mature. You want to wait until 90%+ have turned color, and started to shrink back into the buds. Once that happens, the buds still have 1-3 weeks left. They won't grow much on the outside, but they will be swelling up inside becoming more dense, and increasing weight. Finally after that 1-3 weeks once the bracts(calyxs) look fat and swollen you can check the trichomes and determine when to harvest the plant.