Round back to square back alt

That's a mouth full, and the biggest problem with our old undersized wiring.

Add brighter headlights, stereo, electric fans, etc and zap/smoke!

Old underpowered alternator will just max out at 40 or so amps and things might just get hot!
It's not a problem until someone inadvertently adds load like electric fans. Or adds load to wires and connections that can't handle it
Even then, its not a zap! poof situation, more typically your slow burn (melt) scenario.
The alternator won't care other than it too may get hot from running at near maximum. The battery has a tremendous capacity and will cover for a while.

Lets go over the loads.

Here's what I've measured on my '85 AMC Jeep SJ (with Delco 12SI alternator so field current is internal)
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The Delco alternator was rated 74 amps or later 92 amps. It only put out 27.4 amps. Why?
Because that's all the loads that were turned on or connected.

A 64 Barracuda will have about 2.5 amps for the ignition and about the same for the field. Lets call it 5 amps
Headlights will be about the same, 9 amps. A little less if using the original lamps, or the 35 W low beam halogens.
Parking and instrument lights will be less since it has no side markers. lets call it 5 amps for simplicity.
Heater fan will probably be the same or less. Lets call it 9 amps.
Total current needed driving on a cold night, 27 amps.
Well within the capacity of a '34 amp' alternator at high idle or driving down the road.

The one load not listed is battery recharging. If the battery wants 10 amps (such as after starting), then the '34 amp' alternator will not be able to do that at slow idle and run all the stuff listed above. I don't have slow idle measurements for maximum power capacity for any unmolested Chrysler alternator of this period. But it is not uncommon for A-body owners to comment on the fact that the ammeter will flick slightly toward battery discharge when at a stop light at night, especially with wipers or heater fan running. And yes rear brake lights add a few amps to the load.