The fusible link melted because the alternator diodes were momentarily forward biased when the battery cables were reversed, creating a direct short to ground through the alternator. The fusible link melted protecting the alternator. The fusible link is the ~6" length of 16-gauge fusible wire that runs between the firewall junction block and the splice with the two 12-gauge red wires. The polyurethane cylinder enshrouding the three-wire junction just insulates the splice.
Disconnect the battery ground cable. Cut the two 12-gauge red wires where they exit the splice. Disconnect the fusible wire from the junction block and discard it. Procure a 6" length of 16-gauge fusible wire and parallel- or butt-splice it to the two 12-gauge red wires. If the 12-gauge wire strands are coated in dark reddish-brown tarnish, burnish the wires until they appear bright and shiny. Crimp then solder the splice using electrical grade 60/40 rosin core solder. Insulate the splice with marine grade, adhesive lined, dual wall, polyolefin heat shrink, ensuring that the heat shrink extends 3/8" - 1/2" beyond both ends of the splice. Crimp, solder and shrink-seal a new ring terminal to the free end of the link, then attach it to the junction block. Reconnect the battery ground cable and you should be good to go.
For supplemental information on fusible links, read
Fuses and Circuit Protection and
How to make a fusible link.