Time crystals are systems whose properties are periodically modulated in time. Among these, Floquet time crystals exhibit momentum gaps in their band structures, analogous to energy gaps in spatial crystals. Recently, time defects with a ${\pi}$ -shift in the time modulation have been introduced theoretically as temporal analogues of spatial topological defects associated with localized edge modes. Here we perform experiments in a time periodic system using Faraday instability, a parametric excitation of a liquid bath by vertical shaking. Although time defects also trigger an exponentially decaying wave, we show that the analogy does not hold due to temporal causality and lack of energy conservation. However, these time defects provide an original way to explore momentum gaps and reveal their overdamped modes.