What ruse does the “Republican” sniper use to shoot the other sniper?

In Liam O'Flaherty's short story, "The Sniper," a soldier is alone on a rooftop in the middle of a street battle during the Irish Civll War. The sniper is a "Republican," meaning he sides with the forces of those who were against the Anglo-Irish treaty. They wanted complete autonomy for Ireland. His opponents were "Free-Staters." They agreed to the treaty which kept Ireland as part of the British Commonwealth.

The Republican sniper is surrounded by his enemies. Simply lighting a cigarette is dangerous as it reveals his position to an opposing Free-State sniper who takes a shot at him. And, after killing a woman and an armored car commander, he is shot in the arm by the enemy sniper. He then devises a way (a "ruse") to get his opponent to reveal himself. He puts his cap over the muzzle of his rifle and raises it above the "parapet" of the roof. When the enemy takes a shot at the cap, the Republican sniper drops the rifle to the street below. Thinking he has killed his enemy, the Free-State sniper stands up on the opposite roof. He is promptly killed by the Republican. The story's surprise ending is quite sad as the sniper discovers the man he has killed was actually his brother.