Sorry... I've been preoccupied with life lately.
Most of the nerves mentioned cannot directly be accessed unless you're in the O.R.
The phrenic nerve is deep in the chest. It sends signals from the brain stem to the diaphragm, which controls your breathing. You can however slam someone at the diaphragm level and stimulate the nerve plexus in the diaphragm. The vernacular is getting the wind knocked out of you.
The easiest access to a vasovagal response is hitting the carotid sinus. There's one of those on either side of the neck. You can find it by feeling for a pulse. The branching of the carotid artery has both baroreceptors (pressure sensors) and chemoreceptors (CO2 level sensors). Whacking someone at the carotid sinus (the crotch of the bifurcation) sends an indiscriminate signal to the medulla, telling it that the blood pressure is too high or some other crazy message. (Hence the vasovagal or fainting response.)
Most people won't be knocked out by this. There are a few cases written up in medical journals were someone will have a hypersensitive response, and pass out while shaving his neck with an electric razor. But that's the exception and not the rule.
My favorite philosophy is considering these strikes to be like poison on the tip of your spear. If you hit with sound mechanics, then you have something that might work no matter what. If you hit with sound mechanics AND you make someone slightly vasovagal, well now you have something. A good example is one of Rory's entering techniques, which is nothing more than the forward movement of the arm into horse stance before executing the Seisan jump. In kata you rub your right radial bone on the left arm while going forward. In practice you shear that arm across the neck at the level of the carotid sinus. It's a mechanically sound way to enter someone's space, as it likely results in the person being unbalanced. A bit of a vasovagal response can add caffeine to the unbalancing effect.
A very practical technique in the neck area is triggering the gag reflex. This can be accomplished by poking in the suprasternal notch. Supra-sternal means above sternum. The notch is evident. Just take your thumb or finger and push in there, and you'll feel the urge to cough as if something is lodged in your throat. The tissue there is more sensitive to dL/dt than delta L, meaning that to get the maximum effect you want to poke FAST.
I first learned of this technique at camp, where Bruce Siddle was teaching it and used me as his uke. (Bruce's boshiken or thumb strike is special.
) I have been playing with the suprasternal notch for years, and now my fingers find it like a laser-guided missile. You can gently put your hand or hands on someone's chest, and then slip in there before they know it. The goal isn't to knock them out, but rather REALLY distract them. While they are gagging, you can go on to your next technique or techniques. A good example... the thrusting fingers forward before doing the crane knee thrust in Seisan. If you are pushing with both hands on the sternum, they may not feel threatened and may resist. But blindfolded I can slip my hands right up in that notch, and they will be leaning into it. Follow with the crane knee technique and whatever else floats your boat. Or if you're a grappler or LEO, you probably want to get on with a grappling technique while the starch is out of their body.
Those are the stupid-simple ones that folks can play with and not hurt people too badly.