Duncan designed pickups

Typically a 4 wire humbucker pickup will have two wires for each coil - a start and a finish for each. The typical default option for most such pickups is to run the two coils in series - to do so, you put the start of one pickup at ground, connect the finish wires of the two pickups (and leave then floating, ie not connected to anything else), and the use the start wire if the second coil as hot.

A S-D pickup has black and white as one coil and red and green as the second coil. So the typical series arrangement is green as ground, red and white connected together, and black as hot. Here's a reference:

Humbucker Wire Color Translation - Guitar Pickups, Bass Pickups, Pedals

If your red and white wires are connected together, and not connected to anything else, it sounds like you have a typical series humbucker arrangement.

 

More likely the jack socket is worn out.

Red and white normally get twisted together then fixed by a little solder. Other methods are twisted then heat shrink or twisted/ wrap of insulating tape. There's not much goes on in the control cavity would cause the wires to spring apart.