TW, In the first post, you say the headlight comes on weakly, (not weekly?),
when ignition switch is in the "on", position.
Here's what I think is happening IF this is so: INside the generator are 2 field windings. one connects from the relay terminal internally, to the third brush. Sounds like that one is hooked up o.k. The other field winding should be hooked internally from the "switch" terminal, through the winding, to the ground brush terminal, again, inside the generator. However, on this generator, I believe the second field is hooked from the "switch" terminal internally, to the "relay" terminal internally. Hooked this way, with the ignition switch in the "on" position, current from the positive brush in the generator runs through the switched field through this wrong connection, and then out the switch terminal. From there it goes up to the Ign/lighting switch, connecting on the Lights terminal on the switch. The wire to the headlight also connects to this terminal. So the current then flows back through the headlight wire to the headlight. Then through the headlight bulb, and on to ground. Because the current is going through the field coil and then to the headlight, the voltage to the headlight is lowered by the resistance of the field coil, and the bulb lights weakly.
I really think all you're going to have to do is reconnect the switched field coil so that one wire is on the switch terminal, and the other is on the ground brush. Polarity will need to be correct on the connections, but I'd start by assuming that the wire on the switch terminal is correct, and the other lead only needs to be moved to the ground brush. Give it a try.
HOWEVER, if I misread about when the light lights weekly, this is all hogwash, and pay no heed. Except, it does explain how it IS possible for an internal genny connection to make the headlight light weekly, er weakly, Whatever.