As with the heat equation we need sources for wavefields. I prepared a subroutine for stepping forward the HVP operator while adding in sources and used it for the dot-product test. I find the test y'(Ax)=(A'y)'x using random numbers for x and y leads to the expected six digits of numerical accuracy in a 1003 test.
I am not showing the wave stepping subroutine here because it is just like heatsteps() but with minor added complications.