hey man, this is what I realise.
Well the circuit of relay ignition coil, I think it is for the engine cut off, is activated to cut the engine when the alarm is activated.
To make it works one way could be, white cable to +12, one green to +12, the two green cables will function as a bridge, let me explain u, when the car is in acc position (with the key on) this realy will activate so the two green cables will be bridged, and when the alarm is activated this 2 green cables will be not bridged.
So if you found the +12v of source you may cut it and put it to the other green cable.
Well at this point the engine cut off is understand I think.