However, the question is, can you unravel a weave with your eyes closed?

 

The Eye of the World, chapter 49:

... the Aes Sedai stood in the middle of the hilltop with her eyes closed, not even seeming to breathe.

 

I seem to remember you can only channel with your eyes open?

 

I believe that you can CHANNEL and weave with your eyes closed, but the latter is a hell of a lot more difficult and seriously, why would you? But with Aviendha's & Elayne's experience with unweaving the weaves it would seem tres helpful to have your eyes OPEN so you can see all the slippery threads youre dealing with. Perhaps, if she was unweaving the weave, she was getting in the zone to do a difficult task? Or even, the weave for removing residues and assumedly its own residues as well would be fairly complicated so she was readying herself for that?

 

IMO, I do think she was unweaving the residues almost so that they would spread away...kind of like brushing your hair through a really tough knot and that last stroke before its completely gone. kind of a combo of both theories being bandied about.

 

I'm not sure that Moiraine's eyes being closed is signifigant.  Both channeling normally, and unweaving, would be made more complicated by closing one's eyes.