Like several other states, Texas and New York are not part of the Public Land Survey System (PLSS), that's why data for those states don't appear at the page you linked to. Neither state has townships, ranges, or sections of the type you need, those types of areas are found inside the boundaries of the PLSS. New York has townships, but those are not the same thing as a Township in PLSS terms. You can read more here about why the PLSS was created and why those states are not part of it.
You may want to use either Counties or County Subdivisions instead, those are available in NY and TX and their size is comparable to the PLSS units you're looking for. You can get those layers from the US Census.