...it does not even show battery voltage at all when connected.
So this is a problem... It should have some voltage (>= 0.5V), only then the green output will be enabled
First check the Relay if it working or not.
You can do this simple:
1. Disable output (disconnect any load)
2. press SHIFT-DOWN, then enable option "Green Output", confirm by ENTER
3. Enable output (You should hear relay click), check the voltage on the green terminal (should be the same as on red term).
4. Disable output, and disable option "Green Output" (Note: this option disables any charging functionality).
Next check resistors divider (and connections)... see attach
If no problem here, then need to disassemble module, and check connection on the control PCB till MCU pin.
it goes from connector over resistor R40 1K to the MCU pin 14.
I just did not understand how to use this feature.
When you connect the battery to the green terminal, MCU detects some voltage (from battery),
it should be >= 0.5V, then MCU allow to open green terminal.
So if the battery is dead or complete discharged MCU will not detect it.