How do you replace a fusible link?

Would it be okay to splice that in, even though the wires will be different gauges on each side?
Generally not a good idea to use a fuse where a fusible link was located. That would make sense only if completely rewiring with a fusebox on the engine bay side. Even then, a fusible link on the alternator supply is still generally better. That way the alternator can supply full current for short peripods of time while still being protect from short.

The single wire is connected to two wires that have a fusible link and each of them have two different gauge wires on each side of the fusible link. Sorry if I made that confusing earlier.
There’s only two fusible link wires under the hood, so this would probably be too bulky. It’s interesting though.
Actually, based on the photo in your earlier thread and the FSM diagram, there should be 3 fusible links there and as well as a fourth on feed going direct from the battery to the bulkhead connector. First thing is to ID the one that failed and find out why it failed.

For splicing all three together like the factory, one way would be an inline open barrel crimp. Then if you can save big insulator by slicing it off, reinstall that with electric tape.