Using an extremely valuable global data set from Formosa Satellite (FORMOSAT-3)/Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) radio occultation experiment, a comprehensive study has been carried out on the seasonal and longitudinal variations of equatorial ionization anomaly (EIA) and the temporal variation in the hemispheric asymmetry of EIA during the low solar activity period from November 2006 to October 2007. The interesting result observed from this investigation is the local-time-dependent variation in the hemispheric asymmetry of EIA. During the solstices, it has been consistently observed that the EIA crest in the winter hemisphere appears stronger than that in the summer hemisphere during morning to noon hours. In contrast to this, during noon to early afternoon hours, the ionization in the winter EIA crest decreases rapidly, and the crest in the summer hemisphere becomes more intensified than that in the winter hemisphere. Further, this transition of stronger EIA crest from winter hemisphere to summer hemisphere occurs around 1200-1300 LT during the December solstice months and is delayed by a couple of hours (seen around similar to 1400 LT) during June solstice months. The causative neutral and electrodynamical mechanisms are discussed in light of relative contributions from the field-aligned plasma transport due to transequatorial interhemispheric neutral wind, the strength of the equatorial fountain process, and the ion drag effects during different local times and seasons. The results from the Sami2 is Another Model of the Ionosphere (SAMI2) model simulation also exhibit similar local-time-dependent variation in the hemispheric asymmetry of EIA, which further supports our argument. Also, it was observed that the large magnetic declination of the field lines and the four-peaked longitudinal structure of EIA can significantly modulate the interhemispheric asymmetry of EIA even during the equinoxes.