This paper expands on the foundational concept of temporal persistence in biometric systems, specifically focusing on the domain of eye movement biometrics facilitated by machine learning. Unlike previous studies that primarily focused on developing biometric authentication systems, our research delves into the embeddings learned by these systems, particularly examining their temporal persistence, reliability, and biometric efficacy in response to varying input data. Utilizing two publicly available eye-movement datasets, we employed the state-of-the-art Eye Know You Too machine learning pipeline for our analysis. We aim to validate whether the machine learning-derived embeddings in eye movement biometrics mirror the temporal persistence observed in traditional biometrics. Our methodology involved conducting extensive experiments to assess how different lengths and qualities of input data influence the performance of eye movement biometrics more specifically how it impacts the learned embeddings. We also explored the reliability and consistency of the embeddings under varying data conditions. Three key metrics (kendall's coefficient of concordance, intercorrelations, and equal error rate) were employed to quantitatively evaluate our findings. The results reveal while data length significantly impacts the stability of the learned embeddings, however, the intercorrelations among embeddings show minimal effect.