I could be extremely mixed up, but I thought -ego, -a was for masculine animate adjective-noun combinations, with a few food items also included into the mix. Are all eating-related terms also supposed to take -ego, -a? Or am I just completely getting this all wrong?
What you describe is singular masculine animate accusative, whereas in this sentence it's singular masculine inanimate genitive (the two of which look exactly the same). It's just that szukać is one of those verbs that always require genitive.