Considering that the trigeminal nerve is right in the area where you'd have a TMJ flare-up, I wouldn't be surprised either way.  When I get an ear infection, it can often trigger an extra CH or two.  I'm guessing the swelling puts pressure on that nerve, or else it's referred pain from the nerves in my ear.  I've come to believe that the trigeminal nerves are like the Bermuda Triangle of pain for me.  I have to be aggressive in treating any eye, ear, neck, tooth, or jaw pain on that side, lest I get the nerves all worked up.

My first (wrong) diagnosis was TMJ.  My clusters seem to effect my jaw area the most, although the pain is so severe it's hard to say what hurts the most.  Maybe I DO have TMJ along with clusters.  I never gave it any thought, until now.

Yep.  They did the grinding thing, went through an intense TMJ treatment which included shocking my jaw muscles and I wore a bite guard for many years.  Of course none of that helped.  As with many of us, I self-diagnosed clusters by researching sites like this one.

I get what feels like a bad tooth ache (upper jaw - same side) as well a bad tension pain in my neck.  Funny thing is the tooth ache pain ends as abrubtly as the CH - the neck pain lasts a little longer and sometimes needs a bit of help from Ibu.  I think it is the reaction to the CH - not real part of it.