I have a pretty good accounting of Double A's actions; maybe Diana could chip in on Flax's. I don't know that there's anything to be learned, but maybe someone else wants to chew it over.

Day One -- Double A got one of the lamps from the parlor. I don't know if he took any batteries.
Night One, Day Two -- we both went to the living room, along with white_eyes. I don't know what Double A took there; he says nothing. He made no attempt to take the doll that white_eyes and I both wanted.
Night Two, Day Three -- Double A sent orders to follow me, winding up in the Guest Bathroom. We both saw visions of demonic faces during the night. Double A didn't want the night light that I took.
Night Three, Day Four -- To the dining room. AA said he hadn't sent any new orders, thus had followed me again automatically. There were no items here, if there ever were (I'm not aware if anyone has admitted to being in the dining room before we were.) I used the night light.
Night Four -- I decided to remain in the dining room. Centurion was also there and was supposed to have a lit candle, though it's not clear if he did. Not sure what AA did or didn't do in terms of orders, but he was reported as also being in the dining room with us at the start of the night, until his fatal excursion into the kitchen.