From the form of the equation it can be noted that for it’s PAS the matrix of the EFG would be diagonalised and thus Vxz and Vyz would be 0. Since the matrix also has to be traceless one would only need to know Vzz and Vxx or Vyy.
Visually it is clear that the PAS has it’s z coordinate defined by the line connecting the two electrons. This way the system is axially symmetric in this way.