Accurately modelling monsoon onset remains a challenge. We aim to improve understanding of the coupling between the seasonal cycle and the ITCZ location. Additionally, we seek to reconcile convective quasi-equilibrium (CQE) with the energy flux framework on the seasonal time scale. While the energy flux framework has already been shown to be a predictor of ITCZ location, CQE should also apply reasonably well on seasonal timescales given the short timescale associated with convective relaxation of the atmosphere back to a moist adiabat. We find, however, that the surface theta-e maximum precedes the ITCZ by 11-66 days across a series of aqua planet simulations included in the Tropical Rain belts with an Annual cycle and Continent Model Intercomparison Project (TRAC-MIP). We make use of the Model for Prediction Across Scales (MPAS; one of the TRAC-MIP model participants) to analyze the moisture budget as well as to compute the isentropic mass transport to derive the gross moist stability and moisture stratification. We find that there is a rapid transition between the dry and rainy seasons during a period of near-zero Normalized Gross Moist Stability (NGMS) followed by another rapid transition from the rainy season to the dry season where NGMS becomes unstable and grows towards infinity before switching sign. NGMS and moist stratification are in quadrature with one another such that there is a maximum in moist stratification coincident with the near-zero NGMS and rapid transition from dry to rainy seasons. The dry season is characterized by negative NGMS owing to the predominant subsidence diverging both moist entropy and moisture from the atmosphere. Results show that the ITCZ location follows the zero value of NGMS, suggesting that the ITCZ is more closely coupled to fluxes of entropy and moisture than boundary layer theta-e.