Well the wires got swapped over so it no longer lost the memory.
As for the working with ignition off, its up to the radio.
The Brav/marea headunits have a menu where you can choose if the radio stays on or turns off hen you switch off the ignition.
As for aftermarket radios, its up to them how to make the logic behave, some assume the constant power wire is just to keep memory/clock and don't supply enough current to turn on the radio. And therefore make the logic to not turn on the radio unless there is the other power feed.
You could feed the constant power to both of the headunit wires, leaving the ignition activated one disconnected. But then you need to be sure when you use the power button, it actually enters a low power mode.