I am happy to report that the issue has been resolved—by accident, that is. I am sharing this in the hope that this information may help someone else.
Short version:
Removing the battery power for a while must have flushed some gremlins out of the memory of the AK, and both the front and rear TPM sensors work as expected now.
Long version:
OK, so this happened while I was away on holiday. The battery wasn't hooked up to the Kymco factory trickle charger I received with the scooter while I was away. Additionally, I hadn't ridden for about two weeks before the holidays, so after about a month of not using it, the battery went flat. Not the "it would not crank" kind of flat, but the "the dash didn't come up either" kind of flat! I measured 5.5V through the external charge port connector. I thought the battery was toast. Regardless, I plugged in the trickle charger, and after about 30 minutes or so, the voltage climbed up to 10.1V, so then I hooked it up to a dedicated charger. Once the battery was fully recharged, I took the scooter for a ride. On my way out, the tires felt "soft", so I stopped at a gas station half a mile from my home and topped up the tires. Later it turned out I had over-inflated them a bit due to manometer error at the gas station (Front: 2.55 Bars, Rear: 2.9 Bars, instead of 2.4/2.7). Later, while riding and toggling through the menu just to see my average fuel consumption, I noticed there was a pressure reading from both sensors!!!
Maybe the removal of the battery power, combined with the injection of some more air, worked, but it did.
I had already considered removing one of the battery terminals and leaving it overnight, hoping to find a solution to the issue that way. However, I had already made an appointment with the local Kymco dealer to have it serviced. Plus, it seemed too old-school of a solution, and I wasn't at all confident it would do any good. I was also reluctant to dismantle half the scooter just to access the battery.
