A bit of a problem.

Hi hot_shot_guy, if you can post a diagram of your connections showing the relay and any diodes you may have used, I can probably help you figure it out. Also, please include the year, make, and model of the vehicle.

the12volt 

Also, check the output from the alarm (With a multimeter) that you have wired to one side of the coil of the relay to see if the Alarm's output is staying on or if it's just the relay or some other wiring problem.   I have seen many of the internal small PCB relays they use for Parking Lights output latch up and have seen the actuall contacts of the relay arc together.   But if your using the typical Bosh type relay for a small current load like the dome light,  I don't see you running into that problem.

I'm not to sure how to post diagrams and pics on here yet but i'll explain how I hooked up the illumination output.  First off I have a 1990 dodge shadow and I'm using an UNGO MS2004 Alarm.  The dome light output on the alarm is a BLACK/ WHITE wire and the (-) door trigger wire on the alarm is GREEN.

Relay set-up is as follows..

PIN 30 = to green door trigger input(-) and to negative door pinswitch (yellow on this car)

PIN 87 = Ground

PIN 86 = Fused 12v constant

PIN 85 = to BLACK/ white wire (-) dome light output

Like I said before it was working fine.  Then I tucked the wires under the dash and started my car and went to shut off my car and the dome light stayed on.