need a guru, door switch

hello, I have a 1987 rx-7 and it has negative door triggers to turn on the dome light and door lights. I want to hook up some l.e.d.'s inside that turn on when you open the door, but stay on for a set amount of time after the door is shut. I have the timer aspect all figured out. I tied in to the door pin switch with the positive lead of the l.e.d. Now when I open the door, the dome light comes on, but the l.e.d. does not. When I shut the door, the dome light goes off and the l.e.d. comes on. Meading the l.e.d.'s would be on all the time. So basically I have a + lead when the door is shut, how do I hook this up without using the existing door light circuit? Any help would be great, thank you. I have relays and kinda know how to use 'em. I'm not a total rookie. I have hooked up a remote hatch popper, power door locks, alarm, 4 amps, 18 speakers, 3 sirens, l.e.d. scanner, etc......but this one, I can't figure out.

greg

thank you, thank you, thank you!!!!

greg