Then, last Thursday, the twinges showed up and stuck around. Still not constant, but twinging frequently, sometimes even to the point of being a constant, very low-level ache. So fine -- time to call the dentist. I made an appointment for today; Murphy's Law being what it is, this meant that the pain vanished again entirely yesterday. So this appointment wound up being the typical frustrating attempt to diagnose an intermittent problem.
I explained the situation in detail, along with what I have been able to figure experimentally. (Chewing has no apparent effect on the pain, but head position does: lying on that side makes the problem worse, lying on the other makes it go away.) He poked and prodded around the gums, and hit me with a fascinating little device that tests nerve sensitivity: he puts one hand on me, and an electrical probe on a tooth, and gradually raises the current until the tooth tingles unpleasantly. That demonstrated that the nerves in the teeth themselves are fine -- in fact, they're apparently a bit weird, because the nerve conductivity of each tooth was *exactly* the same, which he says is unusual.
So his best guess is a pinched nerve in my jaw. That fits the diffuse and intermittent nature of the pain, as well as the position of its center. (Which turns out to be almost exactly the location where the nerve bundle exits the jaw and spreads into the gums and lips.) He suspects that something may have gotten pinched when I got my wisdom teeth out a year or so ago, and the twinges are some combination of the nerves getting pinched and healing. Neuralgia always being weird, he suspects that the actual location of the pinch may be the back of the jaw; it's just showing up where it is because of the way the nerve bundle works.
The upshot, both for good and bad, is that there isn't a lot they can do about it, at least not within his skill set. If it becomes horrible, he'll refer me to a specialist for more radical options. But the current best option seems to be "grin and bear it" (so to speak). Which actually isn't terrible: while the twinges are annoying, they're not worse than that -- on the 1-10 pain scale, this is maybe a 2 or 3. The worst of it is worrying about whether there is something Very Wrong, that I need to deal with; knowing that there probably isn't, I suspect I can deal with the annoyance more easily...