OK, I have tested the relay with the heater blower circuit and it definitely works. Also I have checked the current going through it and it's around 150mA which is enough to trigger the switch 30/87: 12V/80Ohm = 0.15A (80Ohm is the resistance of the relay).
Now when I plug the same relay to HRW circuit the current is 2mA and the voltage on 30/87 drops to almost zero (160mV) which would be correct 80Ohm * 2mA = 160mV. This means that there is not enough current to trigger the switch. Without the relay plugged in voltage is around 12V.
Any ideas why is that please ?