There is a VERY old tradition of pins being started from the right side or lock side of the gun. IOW, driven from right to left. To remove them, the pins are drifted from the left to the right.
The huge problem with pins in both the original and repro Brown Bess is the pin was filed flush with the curved sides of the stock. That means both ends of the pins have a curve in them and not flat. So it is not unusual to see the wood around the pins all buggered up on original guns where someone in the past took the pins out.
You may be able to start the pins moving with and extremely short "starter" pin punch and then drive them all the way out with a full length drive pin punch. The problem is that even with an extremely short starter pin punch, it may still slip off the curved edge of the pin and skitter off into and damage the wood around it.
One thing I tried years ago and it works extremely well for me is to take a VERY small carbide burr/cutter in a dremel tool and cut into the curved surface of the pin. Though you can't get the end of the pin flat, you can get it curved inward so a starter pin punch that is slightly smaller than the diameter of the pin will get the pin moving. Once it is moving, you can use the longer/standard drive pin punch. Now you want to hold the stock in a padded vise while you do that so the stock doesn't slip while you are cutting into the sides of each pin.
When the pins are out and before you do anything else, I strongly recommend you file the ends of the pins flat and perpendicular to the length of the pin. THEN mark the pin or wrap masking tape around each pin and write on the tape which pin it is, I.E. back, middle, front, etc.
Now the newly flattened edge pins will not completely fill up the hole in the stock flush with the surface of the wood anymore. No problem. Just center the pin so it is about the same distance from each side of the stock and then fill the little hole left over on each side with beeswax. This is an extremely authentic thing to do as I have seen it on quite a few original guns.
Any questions? Please ask.
Gus