It is shown that the isovector np-pair number operator can be realized in the O(5) quasi-spin basis. The computation of the isovector np-pair number is demonstrated for even-even and odd-odd ds-shell nuclei described by the charge-independent mean field plus isovector pairing model restricted within the O(5) seniority-zero subspace, thereby binding energies and low-lying excited states of these ds-shell nuclei are fit, along with estimates for the isovector neutron-proton pairing contributions. For reasonable neutron-proton pairing strengths the isovector np-pairing energy contribution to the total binding energy in odd-odd N = Z nuclei is systematically larger than that in the even-even nuclei. In sum, the results suggest that the isovector np-pairing mode is favored in odd-odd N = Z nuclei; and additionally, a decrease in the double binding-energy difference for odd-odd nuclei is primarily due to the symmetry and Wigner energy contributions to the binding energy.