Well, after towing the car to Atlanta from Miami, replacing the fuel pump, getting a junkyard carburetor from another 20R, pulling the carb to replace a gasket that sprung a leak, pulling the fuel pump to fix some loose wiring, I FINALLY got the car running! It sounds brand new once it warms up, you'd never imagine that it had been used as a shelf in my Grandmother's garage in Miami for almost 10 years 
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So, I'm super excited, it's the first time I've heard the car run since I was a wee young lad, and it's the first car I've ever had that had more than ugly mechanical issues when I picked it up. So this morning before work I walk passed it and try to start it... no dice.
To backtrack a bit, I had a buddy of mine who's much more electrically inclined than I over to take a look at it as I wasn't getting any fuel pressure. We tested a few things and kept seeing very intermittent issues. As a quick test, we pulled the fuel pump out, dunked it in a bucket of water and jumped it directly to the battery for a second to see if the problem was the pump. Sure enough it worked just fine. (Yes, I did everything I could to get as much water as possible out of it before putting it back in the tank ;)) Well, through the course of our testing the fuel gauge was showing a level. Once we got the car started, the gauge was reading zero. I didn't really think much until it wouldn't start this morning, but sure enough the gauge was working again. Well, I figured I'd try to test this theory that had been dancing around my head all day and tried unplugging the fuel level sender. I got in, turned the key to on and heard the pump prime. I cranked it and sure enough after a couple seconds, it fired right up.
Though I can't find any schematics (because Chiltons is USELESS! and finding a shop manual for a 77 Toyota Celica is proving harder than I imagined), from what we can tell, the pump and the level sender both have a single wire going into them. I'm assuming they both ground through the shell of the tank, so they share a common ground.
What could be causing only 1 of these to work at a time? The problem seems to be on the sender side, but what could it be? Wire fault? A bad ground from a sender that sat in a tank of 9 year old fuel? Other?
