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The fuse link is in series with the battery for protection of everything.
If the start relay comes up and starter does not engage, suspect the starter or it's cable.
Starters with a lot of age wear the brushes and have too light a pressure against the armature.
In removing the starter then having it tested sometimes gives a false indication of being good if the brushes make good enough contact to make the test good after being banged around.
Good luck.
So I replaced the starter, and the relay. The initial problem was the bad relay, however I made the situation worse because I mistakenly put on wire from the alternator to the top post instead of the bottom post. So of course what happened with that was that once the motor we running the alternator was pushing power to the starter this configuration clearly caused the two problems points I observed....
1. Starter was remaining engaged
2. Battery Light came on
By simply not paying attention to the wires when I initially removed them probably caused me to burning up the old starter, but it was also 15 years old so I'm not terrible upset that I spent the time replacing it, I'm just glad I was able to do it myself.
So big thanks to the advice on the page and the picture that was posted because it was review of this forum is where I first noticed the proper wiring configuration.