If you measure good resistance on the coil - across its two wires, disconnected from the harness - the coil is good. Maybe there's some way it could have in-spec resistance and still be no good... I can't imagine one.
Green to ground should of course give continuity, green is the ground wire.
The white wire should go directly from regulator to the field coil - through the engine plug and the bullet connections of course - and it should not have any connection to ground if the wire is disconnected at both ends.
The regulator is getting zero volts and thus is in a "full power" state when key power is off: it can't actually provide power to the field coil but it will connect the white wire directly to black.
Key off, all the electrical devices normally powered from black will have some resistance to ground relative to how much power they use when powered. So it's normal to have continuity to ground from black when power is off, and the white wire will be connected to black by the regulator.So with the white wire connected to the coil, you will see a low resistance to ground. Measuring the resistance of an always on headlight plus one or two ignition coils... looks like a dead short on a typical meter.
