"Could the gag have been to keep the mouth closed, sort of the way a headcloth was used to keep the mouth from hanging open?"
Good point. A few thousand years ago, in Central Asia, the dead were given a sort of old-movie-toothache wrapping to keep the mouth closed after death but before rigor mortis set in. These newly discovered objects could have been for that purpose.
I'm not optimistic about more finds, as the article said that the amount spent to do these digs ahead of the dam completion is miniscule. Too bad, not enough is known of Elam, and much of that comes from foreign sources (the Babylonian Chronicle, the Synchronistic Chronicle).
Gag; a female burial?