The process in which the developmental fate of a cell becomes restricted such that it will develop into a eosinophil cell. A eosinophil is any of the immature or mature forms of a granular leukocyte with a nucleus that usually has two lobes connected by one or more slender threads of chromatin, and cytoplasm containing coarse, round granules that are uniform in size and which can be stained by the dye eosin.