1970 Dodge Dart- No crank or start- Battery draw

With key in Start, power should flow through the yellow wire to flip the relay, and also through the brown (ignition2) wire which connects to the coil.
The brown wire bypasses the the ballast resistor. This is because, as you now know, voltage during start up is already far lower than it will be with the engine running (around 14 V).
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When power flows through the starter relay from the yellow wire (S2) through the neutral safety switch to ground, then the brown wire (S5) to the solenoid in the starter gets energized.
The brown wire's gets power direct from the red wire (A) coming from the battery to the starter relay.
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