No, the green line has to be on (+12V) when the vehicle is charging (ie, engine running).
The SPG32 is merely a relay. Using the common Bosch/Hella etc convention, the green is its #86 terminal & GND its #85 with #30 & #87 being its main/heavy (SPST) contacts.
But irrespective, you need a line that either says the engine is running (or not) or charging (or not).
So what are you intending to use?
If you don't think it's a mere relay, connect 12V across its small terminals. You should hear it click on.
If it were a voltage-sensing (or "smart") isolator, it would only have 3 terminals: the heavy in, heavy out, and GND.