'pH shock', the idea that fish can die just because the pH has changed a few tenths of points, is a complete myth.
if by 'myth' you mean
a few 10ths of a point, then yes, that is nonsense. most fish are not the senstive, even though the pH scale is a logarithmic scale.
but if you have a tank with a pH of say 6.0 and do a 50% water change with hard tap water of a pH of 7.8 or so, your pH will likely go up at almost a full point..which CAN have a detrimental affect, and quickly sometimes..
certain fish, like tinfoil barbs for example, can be quite sensitive to such a change..
now, why did the pH go up? calcium carbonates in the hard water which of course raises your TDS.
and what would be the best way for the average home aquarist to verifiy what happened?
a pH test kit.
its much cheaper than a conductivity meter
it is a simple indicator of what you are saying:
that is the increase in TDS and the accompanying osmotic shock (rapid change in osmotic pressure) that causes all the problems.
its easier to use pH as an indicator of what is happening with the TDS increase/decrease from the change..
PS - where did you hear that a pH change of a few 10ths of a point (say from 7.2 to 7.4) could cause death and destruction. I would argue that for most of our tanks, such a change probably happens every time we do a regular water change...