At no time in the opening sequence of The Rifleman did Chuck Connors stare into the camera. After firing his rifle he turned his head ever so slightly in the general direction of the camera while shifting his eyes slightly also. He did not face the camera nor did he speak to the viewing audience or make any sort of gesture whatsoever to the viewers.
Chuck Connors breaks the 4th wall in the opening credits after he shoots his rifle and then stares into the camera.