just to reiterate what you already posted, I have learned for myself that your focus is high at the onset as you are identifying your target and you are trying to determine how great a threat your primary BG is. (i.e. does he have gun in hand, is somebody in immediate danger from BG, etc..)
At that point your respiration could be going through the roof or you could be not breathing...if you keep training then you could be at the stage that the minute you are conscious that you are doing either of the two extremes, you then consciously hit the "switch" to do minimal breathing to the tan tien (middle focus point), maybe take a deep breath to calm yourself down, then your body relaxes...at that point you are focussing on your front sight to target and back, if you have identified your BG as not immediate threat, then you can relax trigger finger?
Please keep in mind, in civilian self defense, I have not shot anyone...so a little Hawaiian salt is in order, okay?
My experiences have, until recently been mostly unarmed self-defense against weapons, even gun...usually more than one attacker. Some contact type weapons against armed and unarmed BG's, some bladed weapons against weapons, and some handgun(not fired) against multiple and single BG's with weapons and unarmed. (Not counting military experience)
So whatever I say from experience only has been up to pointing a handgun at the BG and getting said BG to surrender and in some cases...they choose not to surrender.
To confirm what you say, though, Dragontooth '73, breathing is minimal, in comparison to everything else that goes on in your mind and body, but controlling the breathing brings mind and body into control.
Just flow the chi through hand and gun as an extension of the hand, much like when you did the unbendable arm in aikido...chi rooted into the ground, flow through the tan tien and into arm and beyond hand. Focus is light and awareness should be around you once you have determined BG is not immediate threat.
Simple, n'est pas?