We present measurements of [S iii]λλ9069,9531 for a sample of z ∼ 1.5 star-forming galaxies, the first representative sample with measurements of these lines at z 0.1. We employ the line ratio S 32 ≡[S iii]λλ9069,9531/[S ii]λλ6716,6731 as a novel probe of evolving ISM conditions. Since this ratio includes the low-ionization line [S ii], it is crucial that the effects of diffuse ionized gas (DIG) on emission-line ratios be accounted for in z ∼ 0 galaxy spectra, or else that comparisons be made to samples of local H ii regions in which DIG emission is not present. We find that S 32 decreases with increasing stellar mass at both z ∼ 1.5 and z ∼ 0, but with a shallow slope suggesting S 32 has a weak dependence on metallicity, in contrast with [O iii]/[O ii] that displays a strong metallicity dependence. As a result, S 32 only mildly evolves with redshift at fixed stellar mass. The z ∼ 1.5 sample is systematically offset towards lower S 32 and higher [S ii]/Hα at fixed [O iii]/Hβ relative to z = 0 H ii regions. We find that such trends can be explained by a scenario in which the ionizing spectrum is harder at fixed O/H with increasing redshift, but are inconsistent with an increase in ionization parameter at fixed O/H. This analysis demonstrates the advantages of expanding beyond the strongest rest-optical lines for evolutionary studies, and the particular utility of [S iii] for characterizing evolving ISM conditions and stellar compositions. These measurements provide a basis for estimating [S iii] line strengths for high-redshift galaxies, a line that the James Webb Space Telescope will measure out to z ∼ 5.5.