Bird Identification: female Purple Finch or some kind of juvi sparrow?, 1 by Elphaba

Elphaba wrote:
OK, it's dark gray outside and this bird only went to the feeder furthest from the house. I immediately thought female Purple Finch, but I suppose it could be a type of sparrow too. I had been looking at house finches, so I had them on the brain. Did not seem to have any coloring but then there is very little sunlight out there so hard to tell. The eyestripe was pronounced and looked white. The barring on the sides of the chest was very dark and obvious. When I saw it perched facing me, the throat and center of the belly appeared white but then in one of these photos it looks barred too. Also, only a small bird can get inside that cage -- cardinals and red-winged blackbirds for instance do not go in there.

Can you tell at all from these 4 horrible photos?