hello and welcome! that's a great looking guitar.
It's not totally clear from the photos exactly what is going on but it should be easy enough to decipher the problem
there are excellent wiring diagrams on the seymour duncan website HERE
you will need to convert the colour codes on the seymour duncan site to the jackson version, there is a great page HERE with all the different colour codes on.
i would follow the wiring for each pickup and see if it differs anywhere, it is most likely just a bad connection or a loose wire.
do you own a multimeter? if the wiring looks ok then checking the resistance of the pickup is the next test. if you don't have the kit then it's time to find a tech, fi you give us an approximate loation then someone might be able to suggest one, or even offer to look at it for you.
Matt
EDIT - the switch is another possible issue, they are prone to getting dirt/corrosion on the contacts, give it a good few switches and see if that makes a difference, it might be worth cleaning the contacts, just pulling a strip of brown paper through them can be enough to get them working again.