For the proof I've read that verifies transverse electromagnetic waves are consistent with Gauss' Law, there seems to be the suggestion that the magnetic and electric field at a given small length c(dt), along which the waves travel, propagate infinitely backwards and forwards in their respective axis. In this way, the same electric or magnetic flux enters one side of the surface as exits an adjacent parallel surface. I assume then that there is no way to set up a Gaussian surface so that a "source" either wave is inside the surface, meaning that the waves have to infinitely propagate on a certain axis at any given instant, right? Otherwise I don't think I totally understand the proof. While I'm on the subject, I also am unsure if EM waves leave a trail going from there point of propagation forward, back to their source. Or is this only the case if the source is continually emitting the waves? Thanks in advance for any clarification.
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