This paper presents forecast and investigation of the variation in ionospheric Total Electron Content (TEC) during the solar eclipses (SEs) of December 2019 and June 2020 using three different methods: Deep Autoregressive model (DeepAR), Feed-Forward Neural Network (FFNN), and Ordinary Kriging-based Surrogate Model (OKSM), and the TEC data predicted by DeepAR, FFNN, and OKSM were compared with the actual TEC during the observation days. The study was conducted based on GPS data taken from the IISC receiver located in Bangalore, India, during the SEs which happened on 26.12.2019 and 21.06.2020. The TEC data were examined to assess the effect of solar eclipses on TEC values. Eighty-day prior TEC data for the IISC station are gathered from IONOLAB servers along with the other parameter data like Dst, Ap, F10.7, and Kp taken from OMNIWEB servers which were used to predict TEC. The reliability of the forecasted results is evaluated using numerical factors like Normalized Root Mean Square Error (NRMSE), Correlation Coefficient (CC), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and R-squared. The study demonstrates the usefulness of combining multiple methods for analyzing TEC variations during SEs and highlights the potential of OKSM, FFNN, and DeepAR models for studying TEC variation in the same context. The findings may be useful for satellite broadcasting and navigational services and for further research into the influence of solar eclipses on the TEC changes.