Back to the original question, has anyone considered the fact that what the king said was the last words out of his mouth, spoken just seconds before his death? There's a definite possibility that what the king spoke was actually just death-babbling, (perhaps he was channeling Nohadon,) and Szeth simply interpreted it as actually coming from the king's conscious will because 1) it seemed to fit the context and 2) the death-babbling phenomenon seems to have started at right about this same time and Szeth was probably not aware of it yet.
I've considered that, but in a rather different way - there's nothing "just" about "just death babbling". The pre-death blurbs are all full of meaning, prophecy, and supernatural insight, and at least some of them definitively indicate continued awareness of the speaker's present situation and preferences - for example, there's one where one of Taravangian's victims states specifically that he refuses to tell of what he sees because he knows what Taravangian is doing and hates him for it. Thus, Gavilar's request being part of that phenomenon would grant it
more weight, not less.
In fact, I would go so far as to suggest that the death-babbling phenomenon is the original reason for the Shinovar custom of honoring dying requests - it's happened before, or has always been happening, and at some point in ancient history they learned to take special heed of dying words specifically because dying words are backed by more than mortal knowledge. The recent upsurge could be explained by the Everstorm entering the death-viewable future and giving a lot more people something worth actually talking about in their final moments. Maybe death-babbling has been happening for a long time, but few enough people saw anything significant enough to inspire them to speak that no one really noticed.