Need help ordering a timer relay

I have some 12V emergency lights at my home. Using a magnetic door contact and a simple relay I have set them up so they turn on whenever the door is opened. The problem is that they turn off at the instant I close the door. I want them to stay on for 30-60 seconds after I close the door.

I got an Omron H3Y-2 relay from e-bay but I realized it does quite the opposite from what I want, ie once power is applied it closes the relay contacts after the set time. What I want it to do is when power is applied to close the relay contacts immediately and when power is cut to delay opening the contacts by the time set.

What are these relays called and where can I order one?

Ok, I am an idiot.

The H3Y-2 I have now should work all right. All I have to do is change the door contact from NO that is now to NC and use the NO contacts of the relay for turning on the lights.

The first time the relay is powered the lights will turn on for the time set but after that the system will work exactly as I want it.