One thing that may be an issue is how corroded the wiring is. If theres corrosion on the fuse panel the fuses may not be connecting the terminals. Probably the best advice I can give is to go buy an Ohm Meter and that way you can start diagnosing things and checking to see if you have continuity between one side of the fuse and the other. Even a cheap Ohm Meter is worth its weight in gold when working on electrical!

The parking lights should run off the headlight switch itself and are on a seperate circuit then the brakes/turn signals so Im imagining its more to do with broken grounds and corroded wiring.

Even a simple test light works wonders if you have one handy and that can help you trace the wiring to see where the power is going and where it stops.

Good luck, Jeff

My 1953 Chevrolet
1947.1 Gallery
1972 C-10 1/2 Ton & 1972 C-30 1 Ton