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Howdy,
The coil will be OK. The computerized ignition on the LH equipped B23 used in '82 runs without a ballast resistor. The brown wire comes from the starter. It got to the starter from the key switched power side of the fuse block.
I highly recommend finding the fault in the brown wire. Take a look at the ignition primary circuit diagram below. There is no fuse between the coil and the battery on that circuit. If the wire is broken and drifting around, it could contact the block and weld itself there. The weakest link in the circuit (the key switch) then becomes the defacto fuse. You could be walking.

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Mr. Shannon DeWolfe -- (I've taken to using Mr. because my name tends to mislead folks on the WWW. I am a 52 year old fat man
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