yes the green wire is ground, sometimes - the sender is a "variable resistor" to ground, less resistance as engine heats up - if you short that green wire to ground you should see the gauge move ... could be the gauge is bad
"When we tug a single thing in nature, we find it attached to the rest of the world" ~ John Muir "When we tug a single thing on an old truck, we find it falls off" ~ me Some TF series details & TF heater pics