Ensuring Veterans' Smooth Transition Act or the EVEST Act This bill requires the Department of Veterans Affairs (VA) to automatically enroll veterans who are eligible for VA health care into the VA health care system upon the receipt of information from the Defense Manpower Data Center of the Department of Defense that proves eligibility of such veterans for enrollment. The VA must provide a veteran notice that the veteran has been enrolled, instructions on how the veteran may elect to opt out of such enrollment, and instructions for how such veteran may elect to enroll at a later date. Notice or instructions must be provided in a physical copy and, as is practical, in an electronic copy. Additionally, the VA must consider using mass texting capabilities to provide the notice and relevant instructions required by this bill. The provisions of the bill apply to veterans who are discharged or separated from the Armed Forces on or after the date that is 90 days before this bill's enactment. Any veteran who is eligible for automatic enrollment must be able to access an electronic version of the certificate of eligibility and an electronic mechanism to opt out of such enrollment. The Government Accountability Office must report on the best methods for the VA to provide notice regarding a veteran's automatic enrollment in the VA health care system and related instructions.