We present a comprehensive analysis of 2RXP J130159.6−635806, a persistent low-luminosity Be/X-ray pulsar, focusing on its transition to a spin equilibrium state and the discovery of a bimodal luminosity distribution that possibly reveals a new accretion regime. Using data from the NuSTAR, Swift, XMM-Newton, and Chandra observatories, we investigated changes in the pulsar’s timing and spectral properties. After more than 20 years of continuous spin-up, the pulsar’s spin period has stabilized, marking the onset of spin equilibrium. This transition was accompanied by the emergence of a previously unobserved accretion regime at L_bol = (2.0_−1.0^+2.3) × 10³⁴ erg s⁻¹, an order of magnitude lower than its earlier quiescent state. After that, the source occasionally switched between these regimes, remaining in each state for extended periods, with the transition from a luminosity of 10³⁵ erg s⁻¹ to 10³⁴ erg s⁻¹ taking less than 2.3 days. The analysis of the spectral data collected during this new low-luminosity state revealed a two-hump shape that is different from the cutoff power-law spectra observed at higher luminosities. The discovery of pulsations in this state, together with the hard spectral shape, indicates ongoing accretion. We estimate the magnetic field strength to be ∼10¹³ G based on indirect methods. Additionally, we report a hint of a previously undetected ∼90-day orbital period in the system.