Assuming this is a 3G conversion alternator, check the stator wire (the one all by itself) for a good connection. Then check your grounds. I think a leaky diode can cause the same problem, if I'm not mistaken. I'd take it somewhere to have it checked. Most places will do it for free now, anyway.
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Capri306, Moderator, The Mustang Works Online
1979 Mercury Capri, 5.0L -- C4 -- 2.73
1987 Mustang LX Notch 