The ionospheric responses to the total solar eclipse on 2 July 2019 over low latitudes in southern South America are presented. Ionosonde observations were used within the totality path at La Serena (LS: 29.9°S, 71.3°W) and at Tucumán (TU: 26.9°S, 65.4°W) and Jicamarca (JI: 12.0°S, 76.8°W), with 85% and 52% obscuration, respectively. Total electron content (TEC) estimations over the South American continent were analyzed. The ionospheric impact of the eclipse was simulated using the Sheffield University Plasmasphere-Ionosphere Model (SUPIM) at the Instituto Nacional de Pesquisas Espaciais (INPE). The significant variability of the diurnal variations of the various ionospheric characteristics over equatorial and low latitudes on geomagnetically quiet days makes it difficult to unambiguously determine the ionospheric responses to the eclipse. Nonetheless, some specific issues can be derived, mainly using simulation results. The E and F1 layer critical frequencies and densities below 200 km are found to consistently depend on decreasing solar radiation. However, the F1 layer stratification observed at both TU and LS cannot be related to the eclipse or other processes. The F2 layer does not follow the changes in direct solar radiation during the eclipse. The SUPIM-INPE-modeled F region critical frequency and TEC are overestimated before the eclipse at LS and particularly at TU. However, these overestimations are within the observed large day-to-day variability. When an artificial prereversal enhancement is added, the simulations during the eclipse better reproduce the observations at JI, are qualitatively better for LS, and are out of phase for TU. The simulations are consistent with conjugate location effects.