That would be one of the two ammeter connections. You'll have no interior power unless it's jumpered to the black ammeter wire, or connected to an ammeter (that's what the studs on the cluster are.
Here is a simplified diagram, from MAD:
(Scroll down the page) The difference I BELIEVE is that on your older car, the two main battery and charging leads do not go through the bulkhead connector, but, rather, two separate entrances nearby
http://www.madelectrical.com/electricaltech/amp-gauges.shtml
Here's the diagrams from MyMopar:
http://www.mymopar.com/downloads/1963/63ValiantA.jpg
http://www.mymopar.com/downloads/1963/63ValiantB.jpg
On diagram A, find the ammeter down about 2/3 of the page, about the middle horizontally
The black and red represent the heavy red battery, and black charging leads, off to the right to diagram "B"
Follow them up the page and through the bulkhead, and notice that the RED goes to the starter relay. Normally there is a fuse link there. That is the battery supply.
The black goes over to the alternator output stud
Now back to diagram "A", follow the black from the ammeter off to the right to a splice. THIS IS a factory welded splice, taped up in the under--dash harness, and is where power takes off to various places.
The headlight switch headlight power only. (Tail, park, and dash are fed from a fuse separately) (BLACK going up the page)
The ignition switch (RED going down and to the switch
The fuse panel "hot buss" (RED/ TR going off to the other diagram to the fuse panel)
So you can see, if the big RED and big BLACK are disconnected, there will be no power to the car interior.