I've had a volt meter on the car since I bought it. It never goes above 14.4V and often will sit around 13.6 for a while before trying 14.4V. And even when the inverter goes to 14.4V, another measurement at the battery will be lower, sometimes nearly a volt lower, if it's drawing a lot of current. So apparently there's a good deal of resistance on the wires that go clear from the front of the car back to the trunk where the 12V battery compartment is.
Here are the specs. It was around $315 USD, which is incidentally about the same price as the only 12V LA battery I can find for the car in an original size since the only place that carries them is Toyota. No one else sells a 12V for this car.
https://www.litime.com/products/12v-...ithium-battery
PS. This battery is physically bigger than the original, but feels lighter. It barely fits in the battery compartment, but I can get the door closed, so I say it's a good fit.