Disasters frequently disable the electrical grid, jeopardizing communication infrastructure and causing severe disruptions in emergency communications. Ensuring rapid deployment of power sources for base stations (BSs) is therefore critical in post-disaster conditions. This study presents a mixed-integer linear programming (MILP) framework that dispatches a fleet of electric vehicles (EVs) to energize multiple BSs and maximizes population-based temporal communication coverage (people × time). In a case study involving 20 BSs and 10 EVs, the optimization prioritizes early service to densely populated areas and delivers a total of 17,597 people for 228 minutes of communication access. Although the served population gradually declines as the energy of the EV fleet depletes, the connectivity is sustained until 16:34. Results demonstrate that feasible EV–BS assignments and service durations are obtained considering BS power demand, coverage areas, and EV initial energy parameters. The proposed model enables communication availability after disasters without relying on additional fixed power resources.