Veterans Health ID Act This bill directs the Department of Veterans Affairs (VA) to carry out a two-year pilot program under which: (1) eligible veterans may elect to receive hospital care and services at non-VA facilities, and (2) the VA shall reimburse such facilities for the cost of such care and services. An "eligible veteran" is a veteran who: (1) is enrolled in the VA's patient enrollment system, and (2) resides in a geographic area selected by the VA. The VA shall select: (1) one geographic area within each Veterans Integrated Service Network, and (2) NJ-2 as the geographic area for participation in the pilot program for Veterans Integrated Service Network 4. The VA shall: (1) issue a unique identification card to each eligible veteran who elects to receive hospital care and medical services at non-VA facilities under the pilot program, and (2) take steps to ensure that such veterans receive such care and services at such non-VA facilities.