If you are tapping from the LED most likely its a 5V/0V cycle not 5V/open circuit.
You also need to determine if the signal is 0V/open circuit...this can be also the case.
The voltage will be also lower due to current limiting resistor by the time it get to the LED, 2V perhaps. How is the LED connected? signal/0V or +12V/signal? theres a big difference.
Try this circuit :
Put a small diode (1N4148) just after the output of alarm that connect to the LED.
A capacitor from the diode to the ground. A resistor across the capacitor.
The value of the capacitor and resistor is such that it cover the time when the LED is off. The diode ensure that the capacitor is only charged by the flashing signal and never discharged. The resistor does the discharging (try without the resistor first)
You should get a 2V constant across the capacitor/resistor if you get the values correctly. However you cannot get much current out of this circuit, as I said before there must be a limiting resistor in the alarm.
You must then convert this constant 2V into a constant 12V...more to come later...Im late for work
Hope I didnt confused you