hi never cleaned a car harness but im a arborist and my climbing harnes is alwase getting coverd in sap and mud the recomended way of cleaning my harness is hand wash in cool water with mild soap, then rinse. Allow it to dry in a shaded area once dry check all stichng and make shure everythins intact.
i use a special sope power u gan get from any outdoor shop(millets, blacks) for washing north face coats as it doesent contane any bleach or additives.
but as i sad thats for climbing harness but i ues mine every day at height or up to 100ft with no probs
hope that helps in some way
cheers si