This paper makes an attempt to explain the self-sustained thermally-induced oscillations of a two-phase system consisting of an isolated confined liquid-vapor meniscus (a single liquid plug adjoining a vapour bubble) inside a circular capillary tube, the tube length being exposed to a net temperature gradient, thereby creating a continuous cycle of evaporation and condensation, leading to thermally induced auto-oscillations of the meniscus. This system represents the simplest 'unit-cell' version of a pulsating heat pipe (PHP). The fundamental understanding of its transport behavior leading to self-sustained oscillations is vital for building the hitherto non-existent mathematical models of the complete PHP system. First, visualization of the oscillations of the unit-cell has been done under controlled thermal boundary conditions. Here, a unique and novel understanding of the system dynamics has been achieved by real-time synchronization of the internal pressure measurement with high-speed videography. The contact angle hysteresis at the three-phase meniscus contact line during its upward and downward stroke plays a significant role in evaporation and condensation dynamics. Contrary to obvious interpretations, maximum pressure in the vapor bubble is achieved in the downward stroke, rather than the upward stroke. Thus, the system dynamics cannot be compared with gas-compression cycles; the presence of vapor coupled with transient phase-change processes give rise to singular transport phenomena. Such an interpretation of the meniscus motion and the resulting pressure cycles has not been considered by any of the existing mathematical models of PHPs. By simple scaling arguments, it is demonstrated that there is a high probability of metastable states existing in the system, which essentially point towards considering non-equilibrium evaporation and condensation models for predicting the thermal transport. A simple transient analytical model of thermal transport in the liquid film is developed which clearly explains the observed behavior. Existence of non-equilibrium conditions and there underlying effects on system dynamics need further exploration, both experimentally as well as analytically.