Sounds familiar...it could be a lot of things but I put my money on either the rear shock, sway bar bushings/links or one of the arms/links in the rear. There was a big discussion on this topic not too long ago. As a matter of fact, I just changed the rear shocks (Bilstein HD) and one of the links in the rear (based on recommendations from this forum). The bushing in my link were gone!! The difference is night and day. Do a search on "floating 300e' or "rear links/suspension". Not too difficult for a DIY. Good luck.

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J.H.
'86 300E