Norcal510 - sorry I missed you in Scotts Valley. I would love to meet up next time you are down here! Definitely shoot me a PM next time.
Anyways, I started digging into the electrical system over the past few weekends. Turns out the fusebox was in very bad shape. The fuse holders were all very badly corroded, and hence had high resistance, causing them to heat up and melt the fusebox. 5 out of 8 of the fuse holders had fallen out of correct position due to the plastic melting. All but one of the fuses in the fusebox were also too high of a value.
See:

I decided to spend a few hours with pliers, emery cloth, and jewelers files in an attempt to fix the fusebox up a bit. After doing that, I once again had turn signals, fuel pump, and gauges! Much better!
I started testing all of the various electrical systems of the car to make sure the fusebox wasn't getting hot and found that putting the transmission in reverse would cause one of the fuses to get very hot, and no reverse lights would work. So I took apart the reverse lights and found that the passenger side was wired backwards: 12V was connected to the ground and ground was connected to 12V. It looks like the wiring had been spliced a few times back there. Somehow this didn't blow the fuse, but caused some kind of weird current loop that made the fusebox get very hot. I fixed that and we now have reverse lights:

At this point, the fusebox seems to be holding up and the car is able to be driven around. Here's some proof:

I'm getting a replacement fusebox from Rubber Soul as I'm not very confident in the one that I repaired, but the car at least is drivable for now. I also decided to throw on my new steering wheel just to do something fun on the car instead of electrical repairs:

You can also see the nice replica GTR knob that my wonderful girlfriend bought me to replace the ugly aluminum Impul knob that the car had when it arrived from Japan.
That's all for now! I also received some rebuild kits for the Mikunis and would like to attempt that job over the winter sometime.
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1971 Nissan Skyline 2000-GTX, 1985 Renault 5 Turbo II, 1988 BMW M3 2.5L
2004 Subaru Forester XT, 2004 Volkswagen R32