The availability of macroscopic, nearly periodic structures known as eutectics opens a new path for controlling light at wavelength scales determined by the geometrical parameters of these materials and the intrinsic properties of their component phases. Here, we analyze the optical waveguiding properties of eutectic mixtures of alkali halides, formed by close-packed arrangements of aligned cylindrical inclusions. The wavelengths of phonon polaritons in these constituents are conveniently situated in the infrared and are slightly larger than the diameter and separation of the inclusions, typically consisting on single-crystal wires down to submicrometer diameter. We first discuss the gap mode and the guiding properties of metallic cylindrical waveguides in the visible and near-infrared, and in particular we investigate the transition between cylinder touching and non-touching regimes. Then, we demonstrate that these properties can be extended to the mid infrared by means of phonon polaritons. Finally, we analyze the guiding properties of an actual eutectic. For typical eutectic dimensions, we conclude that crosstalk between neighboring cylindrical wires is small, thus providing a promising platform for signal propagation and image analysis in the mid infrared.