Deidara covers his left eye to use the eye scope, a telescope-like device that allows him to see distant objects and targets clearly [2] [4]. He specifically covers this eye to hide the scope and its function, as it has no relation to the counter he uses against genjutsu [1]. Deidara has two natural eyes, with the right one trained to see through genjutsu [6] [7]. The eye scope doesn't affect his ability to see through genjutsu, as it is a separate piece of equipment [1] [7].

It's worth noting that the eye scope is not a replacement for Deidara's actual eye, but an attachment to his left eye [5]. The reason he covers his eye when not in use might be to protect the scope or to prevent it from obstructing his vision [2] [4]. The brain's process of combining images from both eyes doesn't seem to be directly related to Deidara's decision to cover his eye [8].