Actually, it GETs its 12V supply via that plus splice (all fusible links connected) in the engine compartment.
It should work like this:
BRN is like the reference 12V for the alternator regulator (via TAN). The alternator's field is then regulated by the regulator via switched ground (DK GREEN). BRN is switched (output) by the relay.
BLK is directly connected to battery plus (via a fusible link, as a normal fuse was not used in the engine compartment). This is permanently available on the input side of the relay's switch.
DK BLUE and BRN are the two connectors for the relay's coil. They are:
DK BLUE -> switched by the ignition switch (same as e-choke)
BRN -> ground for the relay; the trick is, that they used the starter's plus for this, which in turn is switched to 12V plus only, if you're cranking (via starter relay). So if you're cranking you have 12V plus on both sides of the relay's coil - no short and coil not energized. If your're not cranking AND ignition is on, that wire basically has a ground connection through the starter. For those couple milli amps the starter does not care (it's wires are quite thick and need a couple more amps to turn), but for that small relay it's enough to switch.
That means, if you're cranking, the relay is not switched (open). Otherwise, if ignition is on (no cranking) the relay is switched (closed).
When it switches (closed switch), direct battery voltage is supplied to the alternator regulators input and you'll safely avoid any overcharging of the battery, as there are no further resistances between regulator input and battery. Without that relay, all those little resistances inbetween (connectors, e.g. twice the bulk head, starter switch, splices and so on) are out of the equation. And yes, this setup brings some other problems: the relay needs to work for charging and also yes, the relay and its connectors are a possible "connection-resistance-problem" by itself.
The wire to the fuse box is just ending at a dead fuse slot (nothing going on after the fuse).
At least, that's my theory, based on the above diagram.
But it si pretty close to my setup at my 69's cars: I put a relay on the firewall, switching input for the alternator regulator as well as to ignition. That's quite some amps (approx 5-7 amps for ignition and another 0-5 amps for the alternator) no longer being a hassle on the bulk head connector and interior wire harness.
And the wire harness being neglected dozens of years was one of the main reasons for such cars to light a fire... (too much resistance at connectors, splices and such by some deposits growing more and more until such resistance produces noteworthy heat...)