Charging Problem

It a little over 12 volts just the battery..........
After the engine was just shut off? New battery? Might not be fully charged. Fully charged should be more like 12.5 to 12.8 V with no load, assuming no surface charge.

MSD 6 series pulls about 1 amp per 1000 rpm. In my experience, not usually enough to show on the built in ammeter even when wired to the battery.

Electric fans. IMO if you plan on running them with the engine off, need to change or at least modify from the factory wiring strategy.*
1963 seems like it has more robust bulkhead connectors than many other years.
Even so. Pegging the alternator indicated over 40 amps through those wires.

But we really don't know fully what is going on. If the battery is low, it will suck a lot of amps if you let it. Add that to whatever your fans draw at that voltage and the circuits capacity is exceeded.

*If your car already has the better bulkheads, then what I'd be tempted to do is put the fans on fused relays. When the key is in RUN, the relay closes and the fans get a direct connection from the alternator.
In the meantime, just power your fans from the alternator - with fuses sized for the smallest wire or the equipment. That way your ammeter will actually show the charging situation.