Jumpstart Our Businesses by Supporting Students Act of 2019 or the JOBS Act of 2019 This bill expands student eligibility for Pell Grants by establishing the Job Training Federal Pell Grant program. Specifically, the bill requires the Department of Education to award a job training Pell Grant to a student who does not have a degree; attends an institution of higher education (IHE); is enrolled in a career and technical education program at an IHE that provides 150 to 600 clock hours of instructional time over a period of 8 to 15 weeks and provides training aligned with high-skill, high-wage, or in-demand industry sectors (i.e., job training programs); and meets all other eligibility requirements for a Pell Grant. It also specifies that any period during which a student receives a job training Pell Grant counts toward that student's Pell Grant eligibility period.