The pin you are metering is likely an "open-collector output", which relies on an external lamp to pull the pin high (~12v) when the lamp is off, and the internal transistor pulls the pin low (0.3V) when the lamp is on. Since the connection to the lamp is missing, you are seeing only the 0.3V or nothing.
Temporarily connect a 1K resistor from the output pin to +12V. Then measure the voltages at the output pin as it switches. I'm guessing you will see ~0V, and 12V, respectively. If that works, write back and I'll suggest how to connect a lamp or a LED.
I see the diagram now. Which box are are retaining? what pin (wire color) is the output that should drive the remote LED?
Is it the Blu/Red wire?