Hmm, I would say it's time to check the condition of the 12V auxiliary battery. Might turn out to be something else, but check that first.
A 2 amp charge of the 12v for 12+ hours then a disconnect of the 12v from the system and reconnect would top it off and reset the system, if it still blinked "P" I'd get it to the dealer.
It says that a "problem" is not a "malfunction." But then you still have a "problem", so go see your friendly neighborhood Toyota dealer, who will run some diagnostics and charge you $$$$ to do so and then tell you they couldn't find a "problem." Problem solved! Like you said - clear as mud...