It is very easy to determine if a regulator is working. With engine running the voltage measured on the battery must be 13.5-13.8 volts (or close to that) if it is more than 14volts or less than 13volts your regulator has failed. The regulator is not your problem from what I gather. I would take that previously overheating amp gauge and throw it as far as I could, it is a ticking time bomb (besides it provides absolutely useless and unreliable information even when it was new) Install a volt gauge in its place. Tie the 2 fat wires on the amp gauge together and use them as the + to feed the volt gauge and make sure they have a really good connection. A volt gauge will provide you with all the information you need to know about your electrical system (in respect of the charging status)
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