in 76 my new trans am had a simler problem had a clicking sound since it was new.i took in to the dealer and they changed the entire rear assy.a few months later the noise is back. the service manager told me that gm had a new limited slip oil and that had no whale oil in it.he told me to go to my parts store and buy some old type of l/s oil with whale oil,i did and never had any more trouble.