That wire has to carry the rated output of the alternator---unless you are using it as a fusable link--today with all these high amp alternators and godzilla batteries, fiberglass bodies, rear mounter batteries, powdercoated everything, very few cars are wired adequetly

In most of the cars we work on with electric fans we run a dedicated wire from the alternator to the fan relay so it bypasses most of the system to/from the battery

Anyway put a number 6 to that main cable and also a number 6 from the alternator base to the battery post negative and most of your problems will go away---