On a 124 there is a link that goes more or less horizontally straight forward from the rear axle with a rubber bush on each end. They typically don't last 100K and if bad the car will sway like a drunken sailor. I'd look for that first on a 124 chassis.

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[SIGPIC] Diesel loving autocrossing grandpa Architect. 08 Dodge 3/4 ton with Cummins & six speed; I have had about 35 benzes. I have a 39 Studebaker Coupe Express pickup in which I have had installed a 617 turbo and a five speed manual.[SIGPIC]

..I also have a 427 Cobra replica with an aluminum chassis.