The scene with major Fambrough is very entertaining, but leaves some out from the script I found. In it, Fambrough acts crazy throughout, but gets decidedly worse right after Dunbar leaves, right before the suicide shot that Dunbar hears as the wagon rolls out of town.
In the script, Fambrough leaves the office naked, except for a plumed hat, his sword, and his revolver. (As written, this reminds me of the incident with Edgar Allen Poe, who arrived to duty similarly once, getting himself expelled from West Point.) This is just after the drink he takes when Dunbar leaves which Dunbar sees through the window. He is pursued by Lieutenant Elgin, who wants to return him to the office. Elgin hears an aside comment from the sargeant who calls Fambrough "crazy", just before Fambrough raises the revolver to protect himself from Elgin. Elgin continues to carefully approach, but doesn't get there in time for the suicide which occurs on the parade ground.
Earlier script notes describe Fambrough as having "sad, swollen eyes. He is an army lifer passed over too many times for promotion and right now does not look like a well man" and, "Sweat has broken out all over him. His grooming is awful. His hands are trembling slightly. Something is very wrong with him."
Earlier, the clinking of the glass in the drawer intimates at alcoholism. There is also emphasis about the childish flourishes during filling the form and the signing, with the giggling.