Although maybe not the exact same issue you are describing - yesterday at my tmj dentists - he's a holistic dentist - we were discussing something similar - when he was doing muscle testing on me he asked if I had digestion problems and then asnwered the question himself and said of course you do - you can barely chew and swallow food - then he re-phrased it and asked did I have problems before the tmj pain pain and total dysfunction started and I did - I first started with chronic indigestion with everything I ate and then graduated to taking Rolaids like they were breath mints, had gall bladder attacks, a bout of gout at one point and it worsened once I got new bridges on my front teeth. From there I developed a hiatal (sp?) hernia and acid reflux - surprisingly - or maybe not - once the tmj started and I could no longer chew and swallow and went to a bland soft if not mushy diet, it all went away - only now I was dealing with the tmj pain and jaw dysfunction. He said its really not uncommon for tmj to "silently" cause a host of medical condtions before the "tmj" condition makes itself known.
I am not too familiar with the vegus nerve but if its as you describe and runs through the brain stem - I would think it is possible if the c-spine has been impacted by the tmj dysfunction for it to be compressed or infringed on or disturbed in some way. Maybe in effect it becomes overstimulated and reactionary to what is happening to the c-spine. Its right up there with some drs suggesting MS, dystonia or an autoimmune disease to me when my tmj first started as the commonality of some neurological condtions involves the loss or deterioration of myelin found on nerves that run through the brain stem as well.
So while I can not answer your question with any certainty I myself would not be surprised if there is a realtionship there - and certainly don't think you are insane for considering or asking about it either. Sometimes I think anyone with tmj must be a little insane though - no "sane" person would be able to tolerate what we do.