Where are the fusible links located and how many are there?

That car only has one link, and it is in the line from the alternator to the starter. The easy way to test it is to see if you have battery voltage at the alternator's battery post. If the link has failed there will be no voltage. Your description could be a bad connection or more common is a bad ground. GM likes to use braided ground straps and those have a bad habit of corroding through and causing problems. Another popular issue is the battery terminals and cables, the acid from an older battery leaks into the cable and corrodes the cable inside the insulation. On the outside the cable looks fine but inside there isn't a lot of the wire left.
https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked