Head tremors are fairly common in older cats. Possible causes include problems in the cerebellum (part of the brain that controls movement and coordination) including tumors, focal seizures, inflammation (encephalitis), spinal/disc disease, trauma, drugs (is he taking any? tapazole for example), vestibular disease and the most common, idiopathic (means the cause is unknown )Head tremors are fairly common in older cats. Diagnosis is often elusive. Blood work is a good start and rules out common diseases like diabetes, kidney failure, liver disease and electrolyte imbalances. Was a thyroid hormone (T4) level done? Hyperthyroidism can be associated with head tremors. spinal disc disease can cause tremors. Your observation of inciting tremors by rubbing the neck and jaw may indicate the cervical spine as a factor.
You need to think about how much stress you want to subject your old cat to in relation to neurologic tests to rule out possible causes. Possible tests include plain and possibly contrast x'rays of the spine, spinal fluid analysis to determine if there is inflammation, MRI of the brain and spine, muscle function tests (electromyogram) ...etc.. Unless there is a specific diagnosis suspected and it can be treated, the risk:benefit for the cat and cost:benefit for the owner may make it more reasonable to accept the tremor or try and treat it empirically.
If you wanted to follow through on the neck possibility, plain spinal x'rays would be a place to start. An easy and relatively safe empirical treatment for inflammation including related to cervical disc disease is prednisolone, a corticosteroid, which cats tolerate well.
Talk to your vet about x'rays and/or corticosteroid treatment as a next step if you think it a reasonable option.
Let me know if you have follow up questions.