Fusible link?

A better name for the link would have been Safety Link. It doesn't compare to a fuse at all really. Fuse in its name causes confusion or misinterpretation at least.
A wire is rated/sized to carry a desired amount of current without overheating. A safety link in that wire is typically 2 wire gauge sizes smaller than the wire its protecting ( there is some deception in that too ) . These safety links are always placed outside the cabin to prevent burnin' the beans ( beings ).
So what actual fuse contains a link that compares to the multi strand wire in a safety link ?, none, not even the maxi fuses.
I'm not going to comment on safety link construction other than to say its not the same copper as the wire attached to it. Why that is gets far too complicated for most of us.
I wont add comments on your working on the electrical while hot either. You have already found the faults in that.
There are ways to isolate, diagnose, and repair individual circuits, but nobody knows everything. That's why a dealership service dpt. will have a engine specialist, a trans' specialist, electrical specialist, etc..
Good luck with it.