I thought some '84s still had the single chain, but I guess not .

Anyway, I think your tensioner may not be holding oil pressure over-night

http://www.peachparts.com/shopforum/showthread.php?t=105165&highlight=380sl+chain

http://catalog.eautopartscatalog.com/mercedesshop/sophio/wizard.jsp?partner=mercedesshop&clientid=mercedesshop&baseurl=http://catalog.peachparts.com/&cookieid=1D00YU6RY1D61563ZX&year=1984&make=MB&model=380-SL-002&category=A&part=Timing+Chain+Tensioner