What causes exhaust pipe metal sounding rattle from right rear of 1981 Corvette automatic at 1300 rpm in any gear but no rattle in neutral?

You need to check all the exhaust pipe hangers, one of them is letting the exhaust rattle against something. Also check muffler heat shield it could also be loose. When transmission in engaged in any gear the engine is torqued to the right, so that is moving the exhaust ( it is attached to the engine so it moves with the engine )into a position to rattle, in neutral the engine is sitting evenly in its mounts so no rattle. May want to check engine and trans mounts too.