differential equations – NDSolve boundary condition linking derivatives to different variables

I'm trying to solve a wave equation (2nd order PDE) in z and t but with a boundary condition that connects the partial derivatives of z and t. For this MWE in particular, I think the answer should be zero everywhere, but I'm finally interested in other cases, not trivial ones.

Here is my attempt:

  D[V[z, t], {z, 2}]== D[V[z, t], {x, 2}

Derivative[1, 0][V][0, t]    == derivative[0, 1][V][0, t],
Derivative[1, 0][V][1, t]    == derivative[0, 1][V][1, t]
{t, 0, 1}, {z, 0, 1}

which gives the error:

NDSolveValue :: fembdnl: The dependent variable in (V ^ (1,0))[0,t]== (V ^ (0,1))[0,t] in the boundary condition DirichletCondition[(V^(10))[(V^(10))[(V^(10))[(V^(10))[0,t]== (V ^ (0,1))[0,t], z == 0.]must be linear.

I would appreciate suggestions for better ways to resolve this error, or in general to address the problem. (I realize that the problem can be solved analytically – I try it that way as a step towards a harder problem that will not be solved analytically.)

The application here models an electricity transmission line and I've already tried some approaches, but I have not found one that works.

I use Mathematica 11.3.