I just did this for my '81.
DO NOT MESS WITH THE CABLE MOUNTS!

First remove the front grill and using a hand mirror and light look under the hood latch. You should see a steel wire coming out of the end of the cable and connecting to the latch. The wire is probably rusted through near the latch.

If so, you can buy just the wire with a new handle. Just pull the old wire and handle out, insert the new wire and handle, and reattach to the latch.

I took a look at my recently retired 1980 245 hood release cable. At the handle end the conduit is rigid and just pokes through a grommet in the firewall. In the engine compartment you can't see where it comes through because it's hidden within the "shock tower" extension that runs back to the firewall. There's a void just to the side of the brake booster where a multi wire harness emerges and wraps around the booster. The release cable is hidden by that harness. The cable extends forward under the strut tower and where it emerges it is held down by a small cable clamp. Near the battery, it--and a wire harness--are held down by a larger clamp. Then the cable turns and enters the radiator support and is held by a final clamp before attaching to the hood release. If you are on Long Island you're welcome to come and take a look. - Dave