What Idaho law and the agencies ask you to carry
Two items are required by state law from May 10 through October 20: a properly installed, maintained and working spark arrester on every internal combustion engine, and, for motorcycles, trail bikes and all-terrain vehicles, one serviceable shovel and a water container of at least one gallon.
The rest comes from the road guides. The Forest Service asks Lolo Motorway drivers to pack a forest map, a spare tire, food, water and gas. The BLM’s Owyhee list is plenty of gasoline, bottled water, a first aid kit, a flashlight, a properly inflated spare with lug wrench and jack, extra food and clothing, and a map that shows land ownership. A stove burning liquid petroleum or propane stays legal under both stages of fire restriction, so carry one.