The battery already reads 12.4V the next morning. Chances are this is not a battery issue. This looks like an immobilizer issue to me. It is possible that there is an open wire or wiring connector somewhere, so playing with all connectors that you can reach could solve the problem, but that's a long shot. I had this issue with a new 1988 Mazda and the dealer couldn't find the issue, because it was intermittent. In this case, the car would die irregularly, then restart after it sat a while.
The brightness of an interior light is a kind of voltmeter, depending on its brightness. It can indicate the battery voltage while cranking. An interior light will dim somewhat during engine start, but will stay on even brighter after the engine starts and the alternator kicks in. I do not know if pushing the starter button turns off your interior lights like it does with other electrical systems, in which case this wouldn't work.
If an interior light is off after an attempted start, it is probably a dirty battery terminal causing the issue. If you turn the ignition on without starting the vehicle, with the A/C on, this could draw 25 amps or so. The radio draws about 5 amps. If the interior lights are pretty bright with the ignition, radio, and A/C on, and the engine is off, chances are it is not a battery or a dirty battery terminal that is causing your issue.
I like the idea of disconnecting the battery to reset the car's computers. This could take many hours, so short the disconnected terminal with the other terminal to help the car's computers fully discharge the capacitors contained within. THAT may take 30 minutes or more under some circumstances to fully and completely reset the vehicle computers. Otherwise, such a reset could take a day or more.
For a while, several years ago, I had a problem with the immobilizer on my '99 Odyssey. I got deep into debugging it, and eventually it fixed itself. Probably some posts on that over on the gen2 forum. Some things from that which may be relevant here (not confirmed true on these cars, though):
- the immobilizer system is only used at start. Once the immo check passes and the ECU allows the car to start (in that car, it would allow cranking, but block fuel injectors, ignition, and maybe the fuel pump as well, from memory), it will run until turned off; immo failure will not kill a running engine = would be a big safety issue.
- (if you expect an immo issue, I would get exact confirmation of exactly what that green light should be doing on a working car) On my '99 when the key went to ON, the green light would come on for two seconds while the ECU/immo system did their check for the RFID chip in the key. After that (before and after starting), if the immo check passed, the green light would go out. If the check failed, the green light would flash forever. While driving around, it would remain off. After driving, after removing the key, the green light would flash about 5 times and then go out - as a signal that the immo is re-initialized to prevent starting next time.
- (based on other stuff in this thread, I am suspecting a voltage problem) Good general tip above on noticing light intensity as a voltage indicator, without needing a voltmeter.

A related tip for testing general no-start conditions is to turn the headlights on and watch to see how much they dim while the engine cranks. BTW, a dip to 9 or 10 Volts during cranking may not be a problem, and some amount of dimming should be expected. On a couple of my older German cars, at least, they have a feature where the headlights are automatically switched off while cranking the engine, just so all the juice goes to the starter. My old Porsche, since it thinks it's a lightweight race car; and my old air cooled VW Vanagon because it needed all the help it could get.
