2013 JK No Start

The following text is from my cross-posts to several online forums:
My 2013 JK decided it no longer wanted to start a few days ago. It drove normally right up until I started it at 10:00 p.m. to pull it inside our gate. Ten hours later (8:00 a.m.) it would not start. It made the loud clicking sound you hear on my first recorded attempt with the external battery hooked up. Everything else worked - lights, chimes, door locks, windows, etc. Just loud, slow clicks or pops. Battery tested 12.9 volts at that time.
For the past three days it would not do anything when you pushed buttons on the key except make this pathetic whimper of a horn honk. Locks did not engage or disengage, lights did not come on as usual.
Today (about four days later) I took the Odyssey I use in my TJ (which is out of the vehicle right now) over and hooked it up. I got all the same responses I did the day the JK crapped out: everything works properly, as you can see. But loud, slow clicks or pops instead of the starter trying to engage.
The Odyssey 34-PC1500 measured at 12.9 volts after having done several attempts to start up. The JK battery currently reads at 9.3 volts. I tested my meter against a known-dead battery, which showed 1.1 volts.
Further, the JK will - on occasion - make a LOUD rattling or buzzing sound that last between two and four seconds. It seems to come from behind the driver headlamp, or in that general area. I tried to record that as it is so distinctive and unusual, but it only seems to do it once per day, and I missed that one time. Oh, well.
Any ideas? Starter? Battery cables?
I also have that issue where you hear three different servos spooling or unspooling for hours after the key has been removed. They happen about once every five minutes and come from three distinct places under the dash. (I wait in the JK for my wife when she shops, sometimes for hours.)
If I get in the JK on a day it has not been driven at all and close the door these servos do their thing every five minutes or so. It is like I have some sort of battery draw going on, but it is not that bad, because the battery (when it initially failed to start) read 12.9 volts at the terminals. So I think the battery is fine.
If the battery is fine then the fault is probably not the alternator or the battery would have been discharged. It is probably not the starter unless the JK starter makes noises like the one in this video, which is different from any starter I have ever come across.
And, as you can see there are no codes. When there is enough power for the instrument panel to light up (which there was in this video, even using the JK's own battery @ 9.3 volts) the lightning bolt and ABS icons stay lit, and the CEL blinks after a bit.
Weirdness...
Thanks for the help, folks.