As I wrote previously, if the purification of 2-bromopentane was easy, it would not be sold with a purity of 90-95% (
some manufacturers honestly report that the product contains several percents of 3-bromopentane). You have to consider whether it is worth doing it, and it depends on the quality of the 2-pentanol used. Besides, what is the point of purification, if there is no way to check if it is effective (GC, NMR).
Several decades ago, when very pure 2-bromopentane was needed to study the reaction mechanisms, it was obtained from synthetic 2-pentanol by reacting its tosylate with LiBr or NaBr.