Response inhibition has been widely explored using the stop signal paradigm in the laboratory setting. However, the mechanism that demarcates attentional capture from the motor inhibition process is still unclear. Error monitoring is also involved in the stop signal task. Error responses that do not complete, i.e., partial errors, may require different error monitoring mechanisms relative to an overt error. Thus, in this study, we included a “continue go” (Cont_Go) condition to the stop signal task to investigate the inhibitory control process. To establish the finer difference in error processing (partial vs. full unsuccessful stop (USST)), a grip-force device was used in tandem with electroencephalographic (EEG), and the time-frequency characteristics were computed with Hilbert–Huang transform (HHT). Relative to Cont_Go, HHT results reveal (1) an increased beta and low gamma power for successful stop trials, indicating an electrophysiological index of inhibitory control, (2) an enhanced theta and alpha power for full USST trials that may mirror error processing. Additionally, the higher theta and alpha power observed in partial over full USST trials around 100 ms before the response onset, indicating the early detection of error and the corresponding correction process. Together, this study extends our understanding of the finer motor inhibition control and its dynamic electrophysiological mechanisms.