As far as I know, no one really understands the effects of [most] etchants on a fundamental level, as with other forms of localized corrosion in general. Bryan Webler had a student working on this sort of thing while I was at CMU, but I'm not sure if he had any conclusions. If I had to guess, the glycerol is used as a surfactant/wetting agent that disrupts the layer of water molecules against the metal. This may affect the amount of acid in contact with the metal or the metal dissolution rate into the solution.
Even less helpful: my experience in corrosion research is that everyone's conclusion is "I don't understand it, but everyone else is clearly wrong", so you may get some conflicting answers.
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