So your saying - with your test meter on volts you get a reading ACROSS the alarm pair ? I`d be very worried if I was you
you`ll only get a reading with reference to the 12v or 0v terminal - think about it - if there was 12v ACROSS the alarm relay the ffng fuse would blow everytime the sensor closed wouldnt it
Yes, you will get a reading using a digital volt meter when there is an open circuit as the high impedance of the DVM will not allow enough current to flow in the circuit to pull the voltage down. When the circuit is closed the components allow a small current to flow in the circuit but not a short circuit.
2 little experiments for you to try:
DMM set to volts i.e. open circuit condition:
DMM set to mA i.e. causing a closed circuit condition: