Possible electrical issues in my 64 wagon

Not unless it is the cause of not charging and the battery runs down. The fact is with a good battery, which is "up" (fully charged) you can drive for HOURS in the daytime, and start the car a few times, before any trouble will show. This is older cars, breaker points ignition, and no EFI

If you have NO power, not even headlights or dome lamps, start by REALLY cleaning the battery clamps and terminals. Get yourself a decent battery post cleaner. If that does not do it, the next most likely suspect(s) are the bulkhead connector and ammeter