I did the gargling, singing, and humming as well (and several other exercises I do not seem to recall), but despite my enthusiasm nothing seemed to be all that difference-making for me.
In my case, I do believe the vagus nerve may have been at least partially to blame for several former and current irregularities (ex. inability to ingest fluids orally), but I have no way of knowing.
My muscles are in a near constant state of tension, which I believe is either the cause or the result from an as of yet.. malfunctioning something or other. My immune system is always fighting off something (chronic low white blood cell count), some kind of threat, real or imagined.
Anyway, my better nutritional standing and daily meditation have seemed to help rid my body of the formerly random autonomic behaviors. I'd suggest giving the latter a try, as meditation has been known to relax the vagus nerve (if I am remembering correctly).
H