The accurate automated eye movement classification is gaining importance in the field of human-computer interaction (HCI). The present article aims at the classification of six types of eye movements from electromyogram (EMG) of extraocular muscles (EOM) signals using the Fourier-Bessel series expansion-based empirical wavelet transform (FBSE-EWT) with time and frequency-domain (TAFD) features. The FBSE-EWT of EMG signals results in Fourier-Bessel intrinsic mode functions (FBIMFs), which correspond to the frequency contents in the signal. A hybrid approach is used to select the prominent FBIMFs followed by the statistical and signal complexity-based feature extraction. Furthermore, metaheuristic optimization algorithms are employed to reduce the feature space dimension. The discrimination ability of the reduced feature set is verified by Kruskal-Wallis statistical test. Multiclass support vector machine (MSVM) has been employed for classification. First, the classification has been performed with TAFD features followed by the combination of TAFD and FBSE-EWT-based reduced feature set. The combination of TAFD and FBSE-EWT-based feature set has provided good classification performance. This study demonstrates the efficacy of FBSE-EWT and subsequent metaheuristic feature selection algorithms in classifying the eye movements from EMG of EOM signals. The combination of TAFD and the selected features through salp swarm optimization algorithm has provided maximum classification accuracy of 98.91% with MSVM employing Gaussian and radial basis function kernels. Thus, the proposed approach has the potential to be used in HCI applications involving biomedical signals.