I cannot imagine the wiring for sewage control would be associated with the fridge. Maybe they share a common power source/fuse.
Whenever I have electrical problems RV related or otherwise, and see a mess of "questionable" wiring like you describe, I go though them one by one, soldering the wiring and sealing the exposed using the best insulation method, shrink tubing. Radio Shack sells that tubing. Once soldered and protected like that, it's like there was never a break in the wiring. If the connections to the switches are also poor and corroded, I would consider going the next step and solder the wires directly to them. You simply unsolder them when anything needs replacing. It isn't hard to do, and it guarrantees the wiring and connections are good. If it is still not working as designed, you can rule out the wiring/interconnections and focus directly on the switches and valves themselves.
I would do my best in retaining the sewage management system as designed. When working well, it's great. Just keep it working well.