What is this wire

That's PART OF the ammeter bypass. It bypasses "everything" on "the other side" of the firewall connector and puts the alternator output DIRECTLY to the battery. Yes, IMO, it should be fused. I believe it needs to be at least what the maximum output of the alternator is. Possibly more. More experienced minds will be able to advise better on fuse size. I don't think I'd use fusible link, though. Maybe a maxi fuse.