@SteveJ, I spent some time with the car this morning and I have something interesting to report. I installed the four fusible links on the passengers side strut tower (mine were corroded at the wire connections, so I figured this would just be good maintenance at this point), and put the relay in. Upon turning the key to on, there didn't seem to be any difference whatsoever. I tried actuating the turn signals, and that just seemed like it put more load on the system and made the seatbelt light go off.
I thought about what you had said regarding the fuses, and even though they had tested fine with the fuse tester, I pulled them all out and had a look. Turns out, the inside link of the fuses themselves had what looked like to me, oxidation and/or corrosion. I replaced the fuel pump level fuse, the turn signal fuse (basically what fuses you mentioned are in that fuse box that could be related to my issue).
I turn the key to on, and the car came to life. Brake light was bright and shiny, fuel gauge went up to E (i only have four gallons in the tank assuming it was dry, so the sender might be off), the charge light illuminated on the volt meter, it seemed like the fuses themselves, while they tested good, were causing the issue.
I tried activating the turn signals via the stalk. Left turn signal just illuminates and stays on, the right one will work inside and outside the car. I do not have reverse lights, and the AC blower motor doesn't work.
At this point I started the engine, and the tach was reading about 500~ RPMs.
The engine was behaving exactly how it did before though, running rough and dying when I would attempt to give it throttle. It did however restart when I tried, but I have no idea if it restarting a few times was just coincidental luck.
One thing I did notice though, My thoughts are beginning to shift to the ignition switch as a possible culprit?
I switched the key to ON and pushed/wiggled the key (it stayed in the ON position during this, I didn't change positions of the key physically), and the seatbelt light lost power. I pushed and jiggled it again and the seatbelt light came back on.
I'm glad the fuses turned out to be the cause as to why a lot of things weren't working, but with those seemingly fixed, is it possible the ignition switch is malfunctioning with how it is behaving?
I'm still stumped about the way the engine is running; It starts, but it doesn't run well and will die on throttle like I mentioned.