Using the OEM car charger for my Pixel 2, it charges fine with the car ON. If I turn the car OFF, the dome light slowly BLINKS and the phone acts like someone is unplugging and plugging the charger back in 30 times a second. I don't think the Prius has it where you can leave something plugged into the 12v socket with the car off, which is not a big deal, but I have no clue what makes the dome light slowly blink. If I need to keep the car off a few minutes, like sitting in a parking lot checking my phone, the only way to circumvent this is to unplug the phone. Otherwise I feel like HAL 9000 is in my dome light.
That's my understanding too. But the dome light is live even when the car is off... The fact it's blinking points to a problem... Does the blinking depend on the car being off, or on? Or same with both... Also I have a Pixel2 phone and haven't experienced those problems. Perhaps you charger has a connection issue?
The dome light (and possibly some other internal lights too) is likely designed to come ON and stay ON for something like 30 seconds after the car is turned OFF or until a door is opened. The cigarette lighter power plug typically stays HOT during that interval. So.....it appears that the mechanism responsible for this delay has failed......or is failing.