At release, the Blind Justice stance had a unique idle animation made for it. However this has been broken for a long time now (possibly more than a year). You can see what the unique idle animation used to look like in the GIF below. Notice also how the Warframe holds the sheathed sword with the cutting edge DOWN, as opposed to UP, when equipped with Blind Justice. Try to get that animation in-game now and you'll get the regular one instead.
Credits to MCGamerCZ since it was taken from his