It appears the charging system isn't working: the generator warning light (red) does not light up when the ignition key is turned, and, with the engine running, there is no charge at the battery. The starting circuit is fine and relies on a new Bosch battery, which is how the engine is able to start.
As with absolutely everything on these BMWs, the electrical system is very much its own thing and you just have to accept the logic that produced it and not get bogged down in "why did you do it this way" or "it should have been done like this", or you'll go nuts. Instead, as there are MANY checks to perform it's better to get stuck into troubleshooting and sort this sucker out.
If I understand correctly, the wiring as it relates strictly to the 'GEN' light goes something like this:
Step 1: with the battery disconnected, I removed the front engine cover, then reconnected the battery, turned the ignition key and checked the dashboard. Nothing.
I tried moving the wiring loom that connects the rear of the instrument pod to the headlight but still no light.
I then moved to the stator, disconnected the brushes' terminals and grounded the blue/black wire from the voltage regulator to the body of the stator: this time the light came on nice and bright, indicating that the bulb and all wiring, connections and components up to the brushes is in good working order.
The next thing I checked was the rotor, first by lifting the brushes and insulating them from their slip rings with a strip of rubber. I then tested for continuity from one slip ring to the other and got a reading of about 3.5 ohms, which is acceptable and would suggest that the rotor is also good. Another thing to test is that the rotor winding isn't shorting to its steel housing, so with a probe on one slip ring and the other on the steel casing, we get a reading of 1 meaning infinite resistance. One more thing off the list.
The engine fires up easily but now the 'GEN' light stays on and there's no reading at the battery terminals, meaning it isn't being charged.
Moving on, I removed the diode board and the wiring that connects it to the stator. I checked the wiring first, and the multimeter shows continuity along all three wires, that's good. The single wire that connects the negative output of the diode board to the Y center tap of the stator is also fine:
I checked the brush holder to make sure it was assembled properly as the DF terminal must not find a ground to the stator housing. One more thing off the list.
Checked the wiring from diode board to voltage regulator; not ideal but good enough for now.
I also took a look at the starter relay and cleaned the spade connectors as it was (and still is) showing signs of corrosion. It seems to be working correctly, though as with many of the original components on this machine, it's probably a good idea to check this periodically and be prepared to replace it with a new one if it fails.
With all of the above checks performed, many components inspected, connections cleaned and everything properly back together, I connected the battery, turned the key and the bloody light still wouldn't come on.
I opened up the headlamp and checked the two fuses in the back of the noodle bowl: one was rated 6A, which is wrong, the other 8A, which is correct, except that it was blown. You don't just replace a blown fuse without knowing why it blew in the first place, however this is still a test phase so that's exactly what I did: two new 8A fuses, turn the key, 'GEN' light on like a Christmas tree, it turns off when the revs pick up, and the battery receives about 13.7v