Securing America's Borders Act of 2019 This bill addresses the hiring, training, and retention of Customs and Border Protection (CBP) employees. CBP shall hire a certain number of new Border Patrol agents each fiscal year until there is an equivalent of 26,370 full-time agents. CBP may hire Border Patrol processing coordinators to assist with processing apprehended persons. CBP shall establish a program to provide emergency medical technician (EMT) and paramedic training to selected agents. CBP shall also take efforts to ensure that at least 10% of agents have EMT or paramedic certifications and that such agents are assigned in sufficient numbers to the U.S. southern border. Furthermore, the bill contains provisions to address staffing shortages in rural and remote areas, including by (1) waiving certain hiring-related requirements in some instances; (2) authorizing recruitment, relocation, and retention bonuses, subject to various requirements; and (3) authorizing special pay rates in certain instances. The Department of Homeland Security (DHS) shall establish a CBP Hiring and Retention Innovation Council, which shall report to Congress as to whether a new pay and employee classification system would improve CBP hiring and retention. DHS shall also carry out pilot programs to improve CBP hiring and retention. The bill also requires CBP to make various updates and changes to its comprehensive staffing analysis. The Government Accountability Office shall report to Congress on CBP's efforts to increase the percentage of agents with EMT or paramedic certifications and on CBP's comprehensive staffing analysis.