This study presents a novel Monte Carlo Empirical Orthogonal Function analysis that combines a dense isotopic proxy network with isotope-enabled climate models to study dynamics and variability of South American Monsoon System (SAMS) over past millennium. This analysis reveals that the leading modes of SAMS variability over the past millennium are regionally stable, arising independently of external forcing (solar, volcanic, orbital). Significant enhancement of the SAMS is accompanied by southward displacement of the South Atlantic Convergence Zone during the Little Ice Age, giving rise to a strengthened South American precipitation dipole. Proxy-model comparison demonstrates outstanding mismatches in centennial-scale hydroclimate departures during the Medieval Climate Anomaly and Little Ice Age from the last millennium mean state. The results of last millennium SASM variability contextualizes modern variability of SASM. The identified proxy data-model mismatch raises a key question to climate simulations of SASM variability, which may attract broad attention from paleoclimate modeling community. Moreover, the reported methodology can be applied to paleoclimate problems of various spatial and temporal scales and is of relevance for the broader geoscience community.