Ending Minsc's quest timer

A question came to mind about this that I don't know if I've seen answered. The question is: what condition ends his quest timer? Is it reaching the Gnoll Stronghold map, or is it actually saving Dynaheir?
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Edit: I assume that otherwise you could exploit by just travelling there and then clear off somewhere else... Which would be a bit rough on the big, loveable lummox.