You said "but it will twitch on the load tester".....I would check all your connections again and then try a new battery.

I think you have a bad connection somewhere such as: a body ground; engine to body ground; or even a faulty battery (shorting out internally). I was going to say the alternator because a bad regulator (probably integral in yours) would cause a voltage flucuation like you described. Try new battery......good luck...let me know what you find out.....

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Red 02