In pursuit of understanding structure-property relationships for the melting point depression of binary eutectic mixtures, the influence of the anion on the solid-liquid (S-L) phase behavior was explored for mixtures of glutaric acid + tetraethylammonium chloride, bromide, and iodide. A detailed experimental evaluation of the S-L phase behavior revealed that the eutectic point is shifted toward lower temperatures and higher salt contents upon decreasing the ionic radius. The salt fusion properties were experimentally inaccessible owing to thermal decomposition. The data were inter- and extrapolated using various models for the Gibbs energy of mixing fitted to the glutaric-acid rich side only, which allowed for the assessment of the eutectic point. Fitting the experimental data to a two-parameter Redlich-Kister expansion with Flory entropy, the eutectic depth could be related to the ionic radius of the anion. The anion type, and in particular its size, can therefore be viewed as an important design parameter for the liquid window of other acid and salt-based deep eutectic solvents/systems.