If you want effectively all of the parking lights, front and rear, to come on when the car is running, the easy thing to do would be to pull the parking lamp relay and repurpose it to be triggered by a "hot in Run" circuit. But, if you only want the front lower LEDs to come on, then you would need to disconnect both lights from the rest of the parking lamp circuit (yellow/blue wire at both light assemblies) and power them via a relay from a "hot in Run" circuit. I don't imagine those LEDs draw much current so they should not require a really large or expensive relay.
-Rod
