Keep in mind that much of the area you are asking about experiences freezing temps during winter months, so potable water from any type of cistern/reservoir is shut down, and water lines drained to prevent damage from freezing. That includes the water fountain at Red Box, outside water at Newcomb's Ranch, and the water at Buckthorn Campground, all of which are available sources during summer months. Despite that, snow will do fine in winter when unfrozen.
During summer months there is potable water at Clear Creek, Red Box, Mt. Wilson, Charlton, Chelao, Newcomb's Ranch, and Buckthorn Campground. No water at Cloudburst Summit, Islip Saddle or Dawson Summit, other than a few springs or natural runoff, until you get to Grassy Hollow.
There is no source of water on Upper Big T from Angeles Forest to Angeles Crest, other than the creek, and, to my knowledge, none from where Upper Big T meets Angeles Crest until Charlton Flats or Chelao.