Is he made of metal?

Here's a simpler electrical challenge:

I just noticed that when I turn my car off in the dark, and turn the dome light off, I can see both of the doors' puddle lights glowing EVER so slightly. I have replaced the bulbs with LED boards. They have like 12 LEDs on them or something, and it seems like the first one barely glows. Is there always a very slight electric current flowing through the wiring until the car cuts power completely 20 minutes later?

Yes, this is something that's not uncommon. My friend put LED bulbs in his dome lights and even when the car was off there'd be the slightest glow coming from the diodes. Even after the car cuts off power your lights may still be lit like that. It's nothing that's going to kill your battery, though.