I like the theory that the reason why Kris closes their eyes is because they figured out the search history thing, has a good idea what it contains...
And doesn't want US to see it. Kris in Chapter 2 has gotten better at doing trickery to keep us somewhat under control. They set things up so we'd HAVE to go to the sink where they could take the soul out and do their thing with the tire. I think they have a very good idea how the player/Kris dynamics work.
Maybe it's not that they don't want to see, but that they know if they see it, we'll also know what's in there.