nope no memory or custom instructions or anything. just plain vanilla 4o.
my suspicion is that it’s less a matter of it being consistently correct and more that it has a 50/50 chance every time to come up left. i ran one of my prompts 6-10 times and it came up left every time. Then without changing anything it came up with right twice in a row.
here’s an example where it gets it right but wrong:
it’s misunderstanding the left side of the image as the left side of the man. so what we see on the left side should actually appear on the right side of the image and vice versa.
btw no need to read anything into this as far as politics or whatever. it’s just something that has a well-recognized concept of left and right 
edit: you actually demonstrated this as well on the Dall-E Halloween thread
Yes one could argue that ‘left side’ and ‘right side’ could imply the image but your instructions focused on the skull and face so to me the left side of the skull is a face and the right side is skull. but the image reflects left side skull and right side face.
i’m guessing that for the most part this is all just for curiosity’s sake. especially if most of the time you can re-roll to flip the coin and see if you get the correctly desired sides. or it’s just for fun or a pastime so that it’s really not important which side the skull is on 