Tagged particle fluctuations for TASEP with dynamics restricted by a moving wall

We consider the totally asymmetric simple exclusion process on $\mathbb{Z}$ with step initial condition and with the presence of a rightward-moving wall that prevents the particles from jumping. This model was first studied in [Borodin-Bufetov-Ferrari’21]. We extend their work by determining the limiting distribution of a tagged particle in the case where the wall has influence on its fluctuations in neighbourhoods of multiple macroscopic times.