That's exactly how it was in my 2005, but the last set of "CANBUS error free" LED's I got do not glow under the trace current that goes through the system.
https://smile.amazon.com/gp/product/B01 ... UTF8&psc=1
These are ridiculously bright, which may not be your thing, but it works for me. I hate futzing with gear in my truck in the dark after surfing late or night time mountain biking, so I upgrade every year or two as LED's get brighter.
But as Joao says, the lights do turn themselves off after a while. All years should do that.
FWIW my truck is now all-LED except for the headlights and foglights, where I didn't have great experiences in the past. May try again now that some of the newer kits are adjustable for focal length in the stock housing though.