The Lee Stooges
I have been looking at your great personality study of these noble sons of the South and think I have guessed the situation in that moment you captured for posterity.
The private on the right has just broken wind, suddenly, loudly and violently. He is doing an impromptu jig to ventilate his trousers.
The corporal is in the immediate blast area and has inhaled a massive dose. The look on his face says it all; he is incapable of breath, let alone verbal communication for the immediate future.
The sergeant appears to be upwind (look at the grass) and knows he's safe. He is amused and is probably saying something like, "Y'all shoulda fired tha'un at the yanks, Clovis!"
Can't prove it, but I am sure I am right!