I installed a set of LED parking lights on my '04 back in April. Look nice. My mystery? Well it seems they stay on all the time. Just realized this. Opened my garage door (lights out) and saw a glow. The glow are the l/r leds. I checked the light stalk, everything off. OK, what is gong on?

 

Very common for LEDs. I can't recall the technical reason (it's in a few threads). It's one of the reasons I've removed LEDs put on by the PO.

Here's a thread:
https://www.jaguarforums.com/forum/s...ts-stay-30277/

 

I too had a problem with LEDs. Tried to hook an additional light in the grille to become more visible to oncoming vehicles. Hooked directly to parking lights. The LEDs would not work properly. Blink as per shorting out at a reduced illumination. Thought the old British Electrical Gremlin came alive. Removed lamp. Rich

 

That seems to be normal (for our cars at any rate). However, I'd expect them to go out when the car goes into 'sleep' mode - mine do after about 20 minutes or so.