The easiest way to figure it out is like this

the 3.5 mm plug at the tip will have 3 distinct sections, seperated by
plastic between them

http://www.vandenhul.com/artpap/wiring.htm half way down the page

the two braid from the wires to the RCA plugs are connected together and
then connected to the sleeve of the 3.5 mm plug.

The thin white wire is connected to the tip of the 3.5 mm plug

The thin red wire is connected to the ring of the 3.5 mm plug

Paul