Havana Syndrome Servicemember Support Act This bill requires the Department of Defense (DOD) to establish a cross-functional team to address national security challenges posed by anomalous health incidents and to ensure that individuals affected by such incidents receive timely and comprehensive health care. DOD must brief Congress on the progress of establishing the team and the progress the team has made in carrying out its duties. Additionally, DOD must regularly brief Congress regarding DOD's efforts related to anomalous health incidents.