Fuses control the PCM.
I recently watched a video on YouTube where the mechanic tracked an identical problem to the connector in the tailgate, that connected to the rear wiper. It appeared that water leaked through the rear wiper seal (where the shift exits the tailgate body.)
Water leaked through the deteriorated seal and dripped down onto the connector. (Think drip, drip, drip.)
This caused green crusties (corrosion) to form between adjacent connections on the connector (on the outside, at the top of the connector.)
This fed the 'wiper keep alive current' to an adjacent circuit, which backfed the leakage voltage back to the fuse panel in the engine compartment; which kept the PCM alive. (Took him several hours to track down.)
He was getting just 3 volts (or something lower than battery voltage) in the backfeed; which didn't make any sense.
He found that the crusties acted like a resistor, allowing a reduced amount of battery voltage to be applied to an adjacent wire in the connector, that should be dead when the car was off.
I'd have a close look at the rear wiper seal. If it looks like there's a microscopic gap where the seal exits, I'd get suspicious and pop off the hatchback interior cover and look at the connector. Your car is the right age for a deteriorated wiper body seal.
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