I took a little time to go back to this machine, but just a little. The output of the alternator is pretty steady, even when turning on the limited accessories. This machine doesn't have many. As usual, the voltage drops for a second or two when switching on the accessories, but comes back, so that tells me the VR is probably doing its job. 13.9 is maybe a little low, but part of that is determined by the state of charge of the battery, which in this case is brand new. If no charge is needed, the VR should trim the alternator input down to avoid overcharging or drying out the battery. My suspicions are that the light should be on only if one side of it is more negative than the other, showing that there is actual current flow in a certain direction. Usually a diode controls which way the current flowing make the light come on. As long as the battery is charging, the current balance causes the light to go out since the current is flowing into the battery rather than from it. If the engine and systems are running from the battery, as in the case of an low current from the alternator, the flow is reversed and the diode allow the light to come on.
But if there are relays involved, then it's possible they are faulty or poorly connected, and there could be a leaky diode somewhere. I can and will check all of that. I also have a good starter/alternator shop I can take the alternator to for load testing. I'll put a scope on the output, which will show a bad diode in the rectifier bridge. I can also ground the test tab and see if the voltage comes up. Kind of have my doubts there, but since it's such an easy test, why not...
I've run this machine under accessory load for several hours without depleting the battery, and the alternator output remains a steady 13.9. I don't really see a problem with that. I feel the problem is in the wiring surrounding the indicator light.
Coaldust, thank you for that diagram. It will help me pick my test points.