There should be a wire from the ignition switch to the regulator, it might even be fused. Look for poor connections.
I'm not familiar with the mechanical regulator on your 4400. But my 1100 has a mechanical regulator with an alternator. I had trouble with my regulator. There are usually multiple sections to the regulator, one section is the voltage regulation connected to the Field coil. The Field coil section gets power from the ignition switch. You can take the cover off the regulator and watch it operate. You should see one section sparking away on the field coil as you increase RPM on the engine.
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