Kevan, just take the negative cable off the battery when it is runing. If it continues to run it isn't your alternator. Based on the symptoms it sounds more like your starter, to be more specific, your starter selenoid. I haven't looked at one yet on the Isuzu's but I believe it is integrated into the starter.

1995 Honda Passport;
Some people wait a life time for their ship to sail in, while others simple grab the oars and begin paddling
Yours truely
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