71 dart instrument cluster

Jeppe,
All I can say is somehting is wired incorrectly.

My suggestion is to begin with the wiring from the power supplies (battery and alternator), then check the main feeds (key switch, fuse box always hot, headlights, horn). Once those are defninately connected correctly, then check the key switch out going wires.

For the complete factory wiriing diagram, get a shop manual. You can download a digitized manual from www.mymopar.com under Service Manuals.

The standard power supply for 1970 and 71 is like this.
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Wire A1 is battery feed.
Wire R6 is alternator feed
These connect at welded junction in the harness.
Notice the ammeter indicates power into or out of the battery. Discharge or charging.

The battery and alternator connect feed Three or four wires from the welded junction.
Wire L1 is for the headlights, there is a circuit breaker in the switch.
Wire Q1 goes to a buss in the fuse box. Parking Lights, dome light, and brake light all are on this buss.
Wire J1 goes to the key switch.
In 1971 power for horn, wire H1, is also connected at this main splice.

When the key is in Start position, brown wire J3, Ignition 2, powers the coil; and yellow wire powers the starter relay.
When the key is in Run position, blue wires J2 get power to the coil and the alternator's rotor; and the black accessory wire gets power for the windshield wiper, turn signals, and additional fused circuits.

We will have to look at the specific diagram for your car to learn the wire route to the instrument voltage regulator.
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looks like its spliced into the J2 (run) circuit.
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