Damn! Never mind.
For anyone who has the same symptom: look for a starter interrupt box.
I was sweating and cursing over the car when its owner came along. "Won't start, I'm diagnosing the starter right now," I say. "Can you go turn the key for me?"
She gets in the car and says, "Oh! Look at this! The little light is blinking again!"
The "little light" is an LED on an interrupter box under the dash, the kind that takes a removable IC key on a phono plug.
I always thought it was a cheap dummy, since the car has always started up just fine without the plug going in.
She tells me now that the system went offline in 1997 (!), the light stopped blinking, and it quit requiring the IC key in order to start -- so she just stopped carrying the key and forgot all about it.
VERY fortunately, she kept the spare key. Would have been completely up the creek without it: a tow-in to an alarm shop and probably a fat bill to de-install the system.
I will probably de-install the little mofo myself now -- if it quit working once but left the car usable, Dr. Murphy says it will probably quit again, but this time leave the car stranded out on the ass end of nowhere some rainy cold night.
So all that this little diversion has cost me is, oh, about six hours out of a really nice warm Sunday afternoon when I should have been drinking beer and enjoying the outdoors. Arrrrrrrrrrrrrgh...
Can you commit seppuku with a torque wrench? I'm about to try it.