Tim, sounds like you have at least a couple issues. Let's take this one at a time.
It takes TWO wires to make a circuit, right? We actually have two circuits, one supplied by the battery and the other supplied by the generator.
Yours are NOT connected together. The GEN light confirms this. How? Your battery feeds the key switch. When turned on, the key switch feeds one side of the GEN bulb. The other end of the GEN bulb connects directly to the armature of your generator at the voltage regulator's ARM terminal. The wiring diagram shows this wire as yellow/black.
The diagram further shows, when your voltage regulator's cutout relay closes, the ARMATURE is directly connected to your BATTERY terminal's yellow wire. So, the GEN light is connected between your battery and your generator's armature. That means, it will only shine when there is a voltage DIFFERENCE between the two. When you first turn the key, the GEN light shines because the generator is putting out zero but the battery is at 12. Both are separated from each other by the cutout relay contacts. When generator motion starts, the light becomes dimmer until both gen and batt are the same voltage, then the cutout relay contacts close because those resistors on the back of your regulator allow the cutout coil power to flow to ground which closes the contacts. Now, the battery and armature are connected together.
So far we have not discussed the other wire, your ground wire, because we are on the positive side.
The generator's case is grounded to the engine and you have a separate ground wire connected to the voltage regulator. The battery is grounded to the engine, but where is the body ground? Are you depending on that generator ground to also serve as the body ground? Don't do it. Like modern cars have, install a short wire from your battery's NEG terminal to the radiator support (or somewhere around there).
Without these solid grounds, all the power wires in the world will not make your generator charge the battery.
After grounding is established and you are sure the yellow wire on your regulator is connected to the battery/starter solenoid, take the cover off of the voltage regulator and start the car.
BTW, your starter solenoid should have all the yellow power wires on the battery side and only ONE fat wire on the starter side. Mis-wiring your solenoid will produce your problem.
If the voltage regulator resistors are good, the generator should produce enough power to energize the cutout relay and close the contacts. Then, your gen will charge the battery.
Watch and study my picture in the first post. It's not a simple picture as the cycle takes a long time. - Dave