Word or short phrase for seeing without observing

I'd go for something like absentminded, as in—

I gazed absentmindedly at the man with the goat on a string, not actually registering the oddness of it.

Other options include "dispassionate" etc., but not as good in this situation.

The expression look without seeing is widely used.

Five hundred years ago, Da Vinci said:

People look without seeing, hear without listening, eat without awareness of taste, touch without feeling and talk without thinking."

I'd use mindless observation. From the Oxford Advanced Learner's Dictionary:

mind·less (of an activity) - so simple or repetitive as to be performed automatically without thought or skill.