Blinks in electroencephalography (EEG) are often treated as unwanted artifacts. However, recent studies have demonstrated that blink rate and its variability are important physiological markers to monitor cognitive load, attention, and potential neurological disorders. This paper addresses the critical task of accurate blink detection by evaluating various deep learning models for segmenting EEG signals into involuntary blinks and non-blinks. We present a pipeline for blink detection using 1, 3, or 5 frontal EEG electrodes. The problem is formulated as a sequence-to-sequence task and tested on various deep learning architectures including standard recurrent neural networks, convolutional neural networks (both standard and depth-wise), temporal convolutional networks (TCN), transformer-based models, and hybrid architectures. The models were trained on raw EEG signals with minimal pre-processing. Training and testing was carried out on a public dataset of 31 subjects collected at UCSD. This dataset consisted of 15 healthy participants and 16 patients with Parkinson's disease allowing us to verify the model's robustness to tremor. Out of all models, CNN-RNN hybrid model consistently outperformed other models and achieved the best blink detection accuracy of 93.8%, 95.4% and 95.8% with 1, 3, and 5 channels in the healthy cohort and correspondingly 73.8%, 75.4% and 75.8% in patients with PD. The paper compares neural networks for the task of segmenting EEG recordings to involuntary blinks and no blinks allowing for computing blink rate and other statistics.