Well, open that can of worms then and find it. It's worthy of finding and fixing. It might take a bit.
But true, yep your green wire to the gauge is grounded out somewhere. Hope it's the green wire anyway and not in the printed circuit of the instrument cluster. Usually not a hard fix. The most common places is, the wire gets burnt to a header or exhaust manifold, and then right where the wire goes through the firewall. The grommet sometimes wears, cuts or falls out and then the wire rubs on sheet metal.
And just a tib bit test, it can also be a failed temp sender in the head. To find out, simply unplug the wire from sender, then turn the key on. If the gauge goes to the Zero, then you know the direct ground is a defective sender and it has grounded itself to the head.
