We learn more about the BA in TGS. Thus we might be able to figure out better, who sat in the Supreme Council of the 13 highest BA.

As we know, Alviarin is the Head. Galina was according to her own PoV the second highest BA. Galina also states that she is one of only three women, who know that Alviarin is the Head. Alvirin also confirms this in KoD by saying that only three women on the Supreme Council know her name.

This leads to the conclusion that one of the other two women was Verin, who might have been either the third or fourth highest BA. This would also better explain, how she got all informations.

I think it makes sense that the Council is a mix of AS from each Ajah - maybe though more Reds, because also most BA came from the Red Ajah - and that at least some other members of the Council are AS, who have political power, like Sitters (though we know that Talene wasn't in the Supreme Council). Most members of the Supreme Council probably also stayed in the WT, after the split.

From her PoV in TGS, it seems very likely that Sheriam sat on the Supreme Council, because she considers how much power she got by joining the BA. The same applies to Delana, who considers herself quite powerful. Other members of the Supreme Council might be Moria, Evanellein, Velina (who once flinches, when Alviarin enters Elaida's room, and thus might be the third woman who knows that Alviarin is the Head), Sedore and Duhara. Maybe Careane was a member as well?

I think Liandrin or the other BA in her group are excluded, because it's stated that they got their orders from the Supreme Council. Katerine might have become the replacement for Galina in the Supreme Council, after her return to the WT.

Certainly Verin's notes will deliver further details on the exact structure of the BA in ToM.