1975 Duster Potential Wiring Harness Issue

Demonic and Matt have covered the most likely possibility.

John Mountain said

My turn signals don't work, radio doesn't work, windshield wipers don't work. Occasionally they will all start working for a minute or two then go out again.

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Those three items only work when the key is switched to run or accessory.
Check your owners manual, or a 75 factory shop manual, because the wipers are probably not fused. At least on earlier cars, they have circuit breaker.
If so, then we can say what all have in common is they share the 'accessory'power wire coming out of the ignition switch.
That said, 1975 might have two accessory power wires.

Terms: Accessory is everything not required for running the engine.

John Mountain said

I'm no expert, and my troubleshooting capabilities have about run out so I've come here for help. I'm really hoping it isn't an issue with a bad ground on the wiring harness because this is my daily driver and I really don't want to tear the dashboard apart.

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On these particular items there is probably not a ground wrapped into the harness. Every year and model is different but generally grounds are either direct from the item to the chassis metal or a short wire to the chassis metal.