Potential ignition issues

H'mmm looking in the black magic water - it's a 1964 a-body with a 225. ;)

Two really excellent suggestions above.
1. Alternator wasn't supplying enough power and the battery was low. Result was too little power available to ignition.
2. Damage to feed (aka supply) wire or connection resulted in the fact it couldn't handle the extra load.

So initial checks are pretty easy.
Check the battery condition. Old school - measure the acid. Sealed battery, measure the voltage.
Check if any of the non-key power items work. Dome light, parking lights, headlights. When they are on, the ammeter should show appropriate levels of discharge.

One more - no tools - check is to follow the alternator output wire, and the battery output wires to the bulkhead. Also the battery ground.
If they look like the wires on the ignition switch, clean, fix replace as needed.

Having a multimeter will help in figuring out the problem, but the above will get you started.

As far as what each wire function is. Hold on.