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Thermal non-equilibrium (TNE) is a well-known thermodynamic mechanism, generally studied in coronal loops. These evaporation and condensation cycles are induced by a quasi-steady and stratified heating. Long-period EUV pulsations and coronal rain are two manifestations of TNE. The quasi-periodicity of the cycles is a strong characteristic of TNE as the system dynamically evolves around an equilibrium position that is not reachable. There are recent reports of coronal rain at open-closed boundaries such as fan-spine topologies and pseudo-streamers. However, no definite conclusions were drawn on the physical mechanisms driving these coronal rain events. We report the detection of long-period EUV pulsations and co-spatial recurring coronal rain showers in a pseudo-streamer observed with AIA on board SDO. The magnetic topology and evolution of the pseudo-streamer are studied in detail using a combination of PFSS modeling and EUV dynamics. The 2.5-day event exhibits all the characteristic features of previous TNE events reported in coronal loops: periodic EUV pulses appearing sequentially in the different channels, following the ordering of the peaks in their temperature response, and coronal rain showers appearing toward the end of these cycles. We further show that the TNE cycles in the pseudo-streamer occur not only in the closed field but also in the open field. Our observations support the findings of recent numerical studies showing that TNE can also occur in open field regions and at open-closed boundaries. In parallel, interchange reconnection occurs continuously and non-impulsively all along the open-closed boundary as seen in EUV. The interplay between TNE and interchange reconnection should be studied in detail in future works. This observation opens further perspectives for the understanding of TNE in the solar atmosphere and its potential implications for the solar wind.