Not sure if they're located next to each other on an E-body, but:
Try swapping the signal flasher & hazard flasher plugs.

It would take some "rigging" to use the hazard flasher as a turn signal switch, and why the fronts & rears would behave differently is weird.
If all of the stock harness is there, and not burned/shorted/missing parts, I'd sure be tempted to remove all of the add-on wiring.
Then go through every function one by one.
This is where a FSM comes in handy.