I noticed on the TLX that the rear LED taillights will turn on when I press the unlock button on the fob when the car is parked. Is this the only time the LED taillights will come on? I don't really understand the purpose of having it turn on when parked as opposed to when it's in drive and other cars can see it when behind me?

 

Only when it's dark outside. Probably to help you find the car in a parking lot.

And it's the "running lights" that come on, they are on when the headlights are on.

 

They turn on when you unlock the car so you can see to get into it. When you put it in drive make sure you don't have "Stealth Mode" selected.