Issue getting relay to trigger, coil voltage might be insufficient
If I had to guess, I would bet that T6 and T9 are probably testpoints on the PCB for use by the engineer or technicians at the factory. And I'd double-down on my guess that those testpoints are connected to digital outputs from a microcontroller.

That's just a guess.

But if I'm correct, then attempting to source any significant current out of a MCU's digital output pin will result in failure. Depending on the size of the relay you're using, the coil could need several tens or even hundreds of milliamps. That's more than a typical MCU can source on a digital output.

However, you're not out of luck. If the test points truly go high or low based on the alarm status, you might be able to use the voltage to drive a transistor to do the heavy lifting. You would just need to construct a small circuit on some protoboard (or whatever) that looks something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

M1 is an N-channel MOSFET that needs to chosen such that it can handle the current that the siren will draw. R1 protects the MOSFET's gate from transient spikes and R2 is a pull-down resistor to turn off the transistor when the circuits are not connected.

I'm assuming you have access to a regulated 6V source that's part of the alarm circuitry. If you don't, you can use the 12V battery to drive the relay's coil, but you'll need to get a 12V relay.

Also, I've drawn the ground points as all tied together. However, the battery's ground does not necessarily need to be tied to the alarm circuit's ground. They can be isolated if you so choose.