Your description of the wiring connections sounds right; all we need to do is get the generator charging and I believe you'll be good to go. Take the cover off the voltage regulator and see if the contacts behind the "B" terminal close when the engine is started and the RPM raised somewhat above idle. I'm going to predict that they do not close. Be careful that you don't touch anything inside the regulator as you remove the cover- - - -it's steel, and one momentary short circuit is all it takes to fry stuff inside the regulator.
If the cutout relay is not closing, disconnect the Battery lead from the regulator, and use a piece of clean business card stock or a slice cut from a 3X5 inch index cards to burnish the points, all three sets of them. DO NOT USE A FILE OR SANDPAPER ON THE POINTS! All it takes is a very slight amount of oxidation on the point surfaces to keep the generator from charging. Once that is done, reconnect the Bat. wire, and use a short jumper wire to flash a momentary connection (less than 1 second) from the B terminal of the regulator to the A terminal. You'll get a moderate arc flash- - - -that's normal. Thos "polarizes" the generator, and should make it charge when the engine is started again. Voltage at the Armature terminal of the generator will rise above battery voltage, the cutout relay will close, and current will flow into the battery to keep it charged. Try that procedure, and let us know what the results are. With the generator turning and the cutout relay closed, terminal voltage at the battery should be 13.0 volts or more. When the engine stops, the cutout relay points should open so the battery cannot discharge back through the generator. Be ready to pull a battery cable connector off in case the points stick the first time you shut down, so don't tighten the cable clamps more than snug, at least for now.
Jerry