We develop a semiclassical theory for electron wave packet dynamics in the presence of an inhomogeneous AC electric field. While static electric-field gradients are known to govern charge transport via the quantum metric, we show that AC field gradients generate two additional geometric contributions to the wave-packet-center current that vanish in the DC limit. These responses are governed primarily by two band-geometric quantities: the quantum geometric connection (QGC) and the higher-order connection (HOC). We derive explicit expressions for the resulting AC responses and identify the symmetry conditions under which they arise. In particular, inhomogeneous AC fields can generate an anomalous Hall-like response even in nonmagnetic systems. Applying the theory to Bernal-stacked bilayer graphene, we demonstrate that the QGC- and HOC-induced responses produce potentially observable transverse currents that peak at the band edges. These results show how inhomogeneous AC fields can probe band-geometric quantities beyond the Berry curvature and quantum metric.