The vagus nerve is deeply implicated in hiccups.
The vagus nerve -the wandering nerve- starts in the brain and it goes down all the way to the gut,getting involved with the heart, lungs, mouth, breathing,swallowing, vocal cords...
The hiccup reflex control centeris between C3 and C5 (cervical vertabraes) and that's where the vagus nerve comes in, while another nerve leaves this center going down the diaphragm prompting its contraction in order to breathe in.
Multiple impulses prompt muscles involved in breathing out to get engaged and disengaged and as air comes in, within a fraction of a millisecond a signal is sent to the vocal cords to shut down and this results in experiencing a hiccup (audible and feeling it).
This may sound very bizzare to you but a relatively easy hiccup treatment
is to overstimute the vagus nerve deliberately so other signals to the vocal cords get blocked.
Unfortunately the most effective method is also a bit invasive.
It involves rectal digital stimulation in a circular and slow motion.*
From my own notes stemming from an article in Annals of Emergency Medicine (copywritten) and titled :
"Termination of intractable hiccups with digital rectal massage."
Also: "Stopping persistent hiccups in the adult by endoscopic maneuver".
Thirty-four patients with persistent hiccups (median duration 10 days) were treated by gentle endoscopic massage of the region of the cardia. Hiccups stopped in all cases. Its early recurrence in one patient only required a second massage, which was also effective. This simple technique is recommended for the treatment of persistent hiccups.
---Source: PMID: 8382900---
Note; The latter one requires a knowlegable medical doctor, whereas the former one can be performed by the patient, herself.
Both work on the same principle and are very effective.
I hope this helps, however, please note that my suggestions and comments are not intended as a substitite for medical advice.
Best wishes and please keep me posted.
* I have used the rectal digital stimulation successfully, but I am not at liberty to disclose any details.