I'll keep looking for small signs though during these short exchanges to keep conversation flowing a bit better, if that makes sense?
Take your shots when the opportunity presents itself. Would it have surprised your W if you sat down in the room wher she was on the computer and read a book or magazine. Fine line here cuz you don't want it to seem like you are following here. In my house, we all just congregate in the great room/den b/c that's where the big tv is. So, it is not unusual for me to be in there even after we have the kids down for the night. If W is on her laptop, I will sit in there and pop my laptop open. Or I may read something. I may not even say anything to her. But, I make myself available if she wants to talk. If she doesn't, then I can always get up and leave.
Keep in mind, this isn't an every night thing. And it has to be natural.
Kids are a great topic to discuss b/c everyone loves to talk about their children. Ask open ended questions of your W to get her talking and keep her talking. And when she talks, listen and look her in the eyes.