BaNiS$_2$ is a system dominated by a fourfold Dirac-cone network. We measured the optical conductivity and Landau level spectra of the Dirac nodal lines and quantitatively modeled the response through ab initio calculations. The optical conductivity shows a highly unusual temperature-independent isosbestic line. Magneto-optical spectra show a nearly $sqrt{B}$ behavior, the hallmark of a conical dispersion. BaNiS$_2$ is a simple prototype of a Dirac nodal line semimetal: its Dirac nodal lines are only slightly gapped, and they disperse exclusively along the out-of-plane direction. Our first-principles calculations account for the observed isosbestic conductivity, which terminates in a Van Hove singularity. We argue that such an optical response is universal for Dirac cones, which must connect with each other within the Brillouin zone by breaking their conical shape.