What causes random long white body hairs?
Since it's been so long, I guess a rushed speculative answer might be at least an idea.

DNA gets damaged randomly all the time, and repair mechanisms are in place to fix it. When the damage is too large or of a very complex kind, permanent mutations can develop, and cause disorders such as cells proliferating without control - i.e. tumours.

I could imagine that the same mechanism could result in cells which overproduce keratin (hair) without melanin (pigment), if the associated genes are affected. Considering that trichocytes and melanocytes, the two cell populations at the base of the hair responsible for production, are among the most rapidly proliferating cell types in humans, an increased risk for mutation would not surprise me. I was able to find a few papers on keratin-associated gene clusters by a quick search, but they all seemed to be related to production of fragile hair rather than excessive length.