Ok now I see that you have the correct regulator with the four wire plug in so we can begin troubleshooting. This is the correct wiring for the 63 to 66 charging system and it carries forward into the 67 to 72 in most aspects.
The horn relay is the junction point for the power wires in the system and you need to have the alternator charging wire, a wire from the battery positive post, a wire from the external voltage regulator and a wire to the firewall connector on there. There is also a small 18 gauge wire that connects there and goes into the dash for one side of the ammeter gauge.
If you refer to my diagram of the charging circuit you will see that the brown wire for the regulator comes from the key switch through a light or a resistor and runs to terminal 4 on the regulator. It appears that you have that wired on the regulator correctly. This wire must read 12 volts with the key on in order to excite the fields in the alternator so it can begin charging. This would be a good first check on the no charge problem. I see the ground wire on the regulator to the sheet metal which is also required. It should be grounded to the alternator as well. My picture above shows the ground on the back of the alternator.
The middle wire on the regulator runs to the horn relay junction and that is present also.
The blue and the white wires are on the regulator properly and they run to the alternator gray square plug with the blue to the F and the white to the R terminals.
The brown wire to the key switch is at the very top of this diagram and it is a resistor wire to the firewall connector where it joins with another brown wire which comes from the dash labeled GEN TELL TALE LIGHT. If you have an ammeter in the dash you will not have this brown wire and the resistance wire will connect to the brown wire on the other side of the firewall connector and that wire is the wire to the regulator. Remember you need to see 12 volts on this wire in order for the alternator to charge.
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