That’s the vacuum hose that is supposed to go to the factory fuel petcok. Without it hooked up, your Z will only run in “prime”. Since the factory petcok fails quite often, most of us switch to a Raptor 660 petcok (which has an “off” setting) and cap off the vacuum line. Costs about $25 and worth every penny.
94mm bbk, +4 stroker, Hot Cams, Vertex piston, FMF Power Bomb header and Power Core can, KW black diamond valves/dual springs, FCR39, K&N, Elka long-travel LT fronts and rear, Houser +3, +3/4 LT A-arms, American Star pro xs chromoly tie rods, Dyna non-programable, Tusk +3 axle.