[Paul Thompson 'Hooligan']

As the tach is out of the car at present, a test on another vehicle would be a good idea, preferably an 'older simpler' model having having just points and coil...

Also, the slightly melted insulation on the green wire could have been caused by a slightly loose connector, which in turn would be a bit resistive and then get warm/hot when current is drawn across it. So check for tightness of connections there too.