If you connect to the switch in the door post this is just the earth (ground) for the door lights. I assume that to come on with the door lights you would need to pick up the feed to the them around where it runs through the door post under the dash and use a connection from that to the LED strip, then wire the earth from the strip back to the door post switch line for it to go to ground when the door was open. I am away atm so don't have a wiring diagram to hand.
Alan
Saab 9000 Stg 1
Saab 9000 2.3 FPT Auto
'81 TR7 DHC