I believe this is what your circuit will need to look like. The only detail I am not sure of is exactly where in the old alarm panel’s wiring you were measuring the 13.4V and 0V readings based on the door being opened or closed. I am also not 100% sure about how the old panel’s end of line resistor is wired into the circuit.
Of course, I probably do not have your input pin on the ESP8266 correct. This is just for illustration if you were using D1 as an input pin. Also, there is a chance that adding this circuit to your alarm panel will cause the old panel to think someone has tampered with the wiring, thereby setting off the alarm. You may need to change the voltage-divider resistor values to much higher values, like 100kOhm and 33kOhms. Since I have never had an alarm panel, I am just using my best guess here.
