Hey there,
I also own a R33 GTST with a M80 Mongoose alarm. Yours sounds as if it is wired dodgy as hell! If I unarm mine but dont open any doors, boot bonnet etc it will relock. However if you open any of the doors etc it will not relock but will rearm the immobilisers if the car is not started in that 30 second window.
Your alarm needs to be rewired by the sounds of it! If you can hear a relay constantly "clicking" for about 10 secs after you arm its a good indication that they have selected the wrong ignition circuit to wire into (2 to choose from).
A friend of mine is a car audio installer and he wired mine up explaining all the gadgets as he went (only took 2 hours including the turbo timer module being used and he has never done a skyline before, though has done many of these alarms)
Hope this helps. If you need the manual let me know and I will upload and email to you
Cheers