The Ginsburg-Sands theorem in point-set topology states that every infinite topological space X has an infinite subspace with either the indiscrete, initial segment, final segment, cofinite, or discrete topology. If X is Hausdorff, then the only possibility is that X has an infinite subspace with the discrete topology. Formalized in second-order arithmetic and restricted to countable, second-countable (CSC) spaces, the Ginsburg-Sands theorem for Hausdorff spaces (GST_2) is provable in RCA_0, though the proof is non-uniform. We additionally cast GST_2 as a problem in the Weihrauch degrees and compare GST_2 to two simpler topological problems. We also consider effective notions of discreteness and Hausdorffness, and we investigate effective variations of GST_2.