To answer my own question, they are open on Tuesdays.
I stopped in with some friends for a few quick eats, and we enjoyed everything we ate. This is now my third time here and, while I'd certainly recommend it for a drink and a bite to eat, I'm not sure that I would sit down for another full meal. Most dishes are great on their own but, as a whole, stringing them together just didn't leave me satisfied. I'd definitely recommend giving the fish board and chawanmushi a try.