Replaced the innerds(Southern term for those pieces inside the slave cylinder) of the slave cylinder in the parking lot last year in Pigeon Forge and will offer my opinion. The black stuff is coming from the slave cylinder. With the extreme heat you need a good high wet-boiling point fluid Dot 3 or 4...no silicon. Replace your fluid at least each 3-6 months. (That per the design engineer at Valvoline for their
Synthetic fluid.) Also, check the travel in the slave cylinder. If you set the rod too tight it will bottom out when you have the clutch released and will cause the rubber piece in the slave cylinder to fail...(I did this so I know this is true.) Another thing, for some reason the slave cylinder (which is raw iron on the inside) only requires a small amount of moisture to rust/corode and for some reason moisture will accumulate in this piece.
Good Luck! Been there and done it on my back in the parking lot...not fun!