Fuel Cell Industrial Vehicle Jobs Act of 2013- Amends the Internal Revenue Code to: (1) allow a $4,000 new qualified fuel cell motor vehicle tax credit for motor vehicles weighing not more than 8,500 pounds that are manufactured primarily for use in carrying or towing loads or materials for commercial or industrial purposes (off-highway vehicles); (2) continue the maximum dollar amount of $8,000 for motor vehicles with at least 4 wheels weighing not more than 8,500 pounds that are manufactured primarily for use on public streets, roads and highways; (3) allow an enhanced credit for light (not more than 8,500 pounds) and heavy (more than 8,500 pounds) vehicles if such vehicles' fuel cell systems achieve a specified electricity generation efficiency rating; and (4) allow a new energy tax credit, through December 31, 2018, for qualified fuel cell property that is manufactured for use in powering qualified motive property. Defines "qualified motive property" as property which is manufactured primarily for carrying loads or materials for commercial or industrial purposes not on public streets, road, highways, or rails or operated primarily for recreational purposes.