Thanks for your input everybody!
I think the idea of junk clogging up the sending unit is pretty plausible. The only thing that gives me pause is that when I've had the problem before my first thought was that was happening, and even blowing air through the line didn't seem to do much to rectify it. Sometimes it's been literally blowing by mouth back through the line, and nothing really changed. It might be that so much junk is floating around that it immediately clogs up. When I first started working on this car in 2017 the tank got some attention, but mostly in the form of throwi