The study delves into the characteristics and dynamics of vector square waves in an erbium-doped fiber laser employing a nonlinear optical loop mirror (NOLM). Through experimental investigation, the laser's operational modes, namely stable and periodic pulsating states, are achieved by manipulating polarization controllers (PCs). Within these states, the generation of two square waves with distinct peak power is observed. The vector properties of the pulses are authenticated using a polarized beam splitter (PBS). Furthermore, meticulous adjustment of the PCs reveals phenomena such as multi-pulse periodic breathing and prolonged fluctuations in pulse intensity.