This paper presents an approach for studying Very Low-Frequency Oscillations (VLFOs) between 0.03 and 0.08 Hz that have been observed on Irelands All-Island transmission system. Previous work by Ireland's TSO has found that the occurrence of the VLFO is linked to the generation dispatch of synchronous machines with governor control. This study verifies previous research by Ireland's TSO and analyses sensitivities such as inertia, system frequency and online generator status that causes an increase in VLF mode magnitude. This paper's results are based on 1-second resolution system frequency, metered generation and power system metric data from 1/1/2018 to 1/10/2020. This analysis demonstrates that the VLF oscillatory mode's stability is highly correlated if governors that consistently provide positive damping torque to the VLF mode are not synchronized. The findings from the study are demonstrated on several events on the Irish system using PMU data. The governor-based dissipating energy flow method is used to validate the relationships found from the generator status and system frequency case study.