Ok, if you suspect it may have some thing to do with the interior light, disconnect the alarm module from the door switch (I suspect this is how you wired it up) and make sure the wiring is just like it was before you tapped in.
If the problem goes away and the interior light works again and the siren stays silent when arming the alarm (but of coarse it can't go off when you open the doors) then I have a solution. If not, reply to this thread.
The door switches on my skyline use a 2 wire switch, which means the trigger is not pulled off the chassis. The door switch wire from the alarm module needs to tap straight off the interior light wire. I know it sounds tricky but this is the simplest way I found:
1. pull the plastic cover off the A-pillar on the drivers side
2. Unless you have a sunroof there should be a harness with only three wires
3. Grab a multimeter or a test probe
3. only one off those 3 wires becomes positive when a door opens - test this by sitting in the car with only the drivers door open.
4. test each of the 3 wires for 12v - push the door switch in with a free finger to check if the wire looses 12v when the button is pressed in.
Only one of the 3 wires should do that, that is the wire the alarm goes to.
Let us know if this was the problem and how it went.