you have damaged the wires going to the sensor on the side of the transfer case. Most likely right at the sensor, it is on the passenger side and there is a short in it somewhere.
Backing up only deals with the hubs, not the transfer case. The light is only a reminder, not an indicator. When you pull the lever and put it in 4h or 4l it is a mechanical linkage on the first gens.
Mine used to come on when it was really wet out, but the wires are compleatly off now and I have not had the indicator light for several years. It does not impact the function of the transfer case one bit.
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Still rollin with the South Side Ninja