a pronounced band of rainfall near the equator exists during all seasons driven in part by dynamic convergence

The ITCZ is caused by the convergence of meridional (north/south) winds on the equator. This causes ascent of air and condensation of moisture which feeds back on (strengthens) the circulation.

The ITCZ migrates north and south with the seasons in most of the tropics. In the tropics, seasons are thus defined by the strength of rainfall (location of the ITCZ) not by temperature which changes little from season to season.