The bottom line is these descriptions are man made and subject to change. During British era we were firmly entrenched into South Asia. In Alexander the Great's time we were firmly entrenched in West Asia. In time of Achaemenid Persia were firmly entrenched in West Asia. During the early Moghul period we were entrenched in Central Asia.
Today I think we are drifting away from South Asia as the British period becomes a distent memory. With hardening of the Radcliffe Line and opening of CPEC Pakistan's destiny looks more to north and west. Many of the multinational companies that have Middle Eastern operations and based in ME cover Pakistan as well. Simply because the India operations cannot cover Pakistan. Thus Pakistan comes often within ME operations.