This sounds strange, but humming and singing--maybe the vibration--activate the vagus nerve.

More recently, I read a story in the NY Times that vibration pills were sometimes used to quicken intestinal motility, which is driven by the parasympathetic nervous system (PNS)--for which the vagus nerve is the main conduit. I should know better because I've learned that the autonomic nervous system is strange, but I laughed at the improbability of such a tool--that is, until I realized that I often had to stop during my bike rides at a portable toilet for a bowel movement . . . right after riding a rough section of trail with lots of vibrations! Not sure if the vibrations stimulate the vagus nerve or, maybe more likely, the intestinal tract, but, even if the latter, this process may offer some support for humming and singing.

Anyhow, you may wish to consider broadening your approach beyond the vagus nerve itself to the PNS. Try things to activate the PNS, like square breathing, meditation, prayer or mindfulness, hugging (dogs are fine!), practicing gratitude, and other techniques you'll find on (reliable) internet sites. I do not practice these things because they are virtuous; I practice them for the direct impact that they have on my PNS.

On the last point, consider getting a Fitbit-type device. I got one a couple of months ago. It provides lots of info while you sleep like pulse, respiration rate, oxygenation level, skin temperature and heart rate variability, which is a measure of the different intervals between heart beats, which itself is a measure of the healthy synergy between your rest-and-relax PNS and your fight-or-flee sympathetic nervous system. I've also used my Fitbit as a biofeedback device to check my pulse in real time to see if I'm getting into fight-or-flee w/o justification--like a lion stalking me!!

Gut neural health raises even more issues. I go with probiotics like goat yogurt, goat kefir, and homemade sourdough bread daily. Although I eat lots of fiber, I'm unsure about the scientific support for prebiotics, as such, but I suppose they do no harm. I cook slow and eat slower. And I monitor my consumption of various antinutrients like raffinose and lectins to avoid digestive/neurological distress.

Hope you get some ideas from this. Good luck.