I’ve had good luck using Purple Zep degreaser to get the stuff off of the cables and out of the tubes & guides.
For brushes you can try any of the ’sunroof drain’ brushes that are for sale online or check out the various listings at McMaster-Carr like these:
https://www.mcmaster.com/products/tube-brushes/overall-length~36/overall-length~30-1-2/overall-length~28/overall-length~26/brush-diameter~3-8/brush-diameter~1-2/brush-diameter~1-4/bristle-material~nylon/?s=brass+tube+brushes