Looking through the various "looking at x" tags, we have the well-established looking at viewer and looking at another, then there are various looking at body parts tags and looking at animal... and a whole bunch of looking at various object tags, but no overarching looking at object.
Personally I believe that any act of looking at something in the image is worthy of a tag in itself, and thus propose making a looking at object tag to cover looking at any inanimate object, while avoiding having to make a mass of looking_at_food, looking_at_headphones and looking_at_snow_bunny* style tags (which themselves would be useless for finding images where a character is simply looking at anything).
Some of the looking_at_x tags have distinct enough implications that they should keep their tags and these should be implicated to looking at object, such as looking at phone, looking at mirror, looking at screen, looking at watch and looking at map. But others, like looking at cup, could probably just be folded in to the general looking at object tag. I would also argue that something like reading should imply looking at object - this may look like it would flood the tag, but there are a lot of images of someone looking at something that currently aren't tagged to represent this in any way so it wouldn't in the long run.
For the tag to count, the object would have to be visible in the image, and the character would have to be visibly looking at the object in question - neither of these things should be merely implied.
*There's a surprisingly large number of images with this one.