Tackle only one problem at a time. That way it will not overwhelm you.
Some photos will help us "help you"! My motor is stock and I have all the vacuum lines just like they came from the factory, so maybe I can help you in that department.
I recommend getting a factory service manual. I have a service manual for the 1984 model, so I can look up stuff to help you, but you really should look for your own so you can refer to it often.
I don't know much about carbs, but I bet your dirty gas tank has a lot to do with the poor carb performance. Drop the tank and clean it out with solvent. Better than that would be to have a radiator shop boil it and then you know it's clean. Blow out the fuel line with compressed air and then change the fuel filter. After you have cleaned up the fuel system from the tank to the carb, THEN you can mess with adjusting or cleaning or rebuilding the carb.
Depending on how much cash you can get your hands on, you might want to consider getting a Weber carb as a replacement/upgrade to your stock carb. It gets rid of all the vacuum lines except the vacuum advance line.
The tail lights should not be too hard if you can find the wires and trace them to the fuse box. I doubt very much that anyone would have monkeyed with the wires unless they spliced in a trailer light connection improperly.
My '86 720 doesn't have a thermostat (removed by previous owner) and she runs great, but I live in SC and the weather here is mild most of the winter.
I'm repeating myself, but pick one problem to solve at a time and choose the easiest ones first so you can still drive the truck. I suggest the tail lights first so she will be legal!
