Alternator light won't come off

The alternator light stays on even though I measure 14V at the battery poles at 3000 rpm.
Background: 1981 380SE (W 126). Noted a morning a few days ago that the
starter hesitated, like the battery was nearly empty, before turning the engine over. Was in a hurry driving the kids to school and forgot about it. Yesterday morning the battery was completely dead. Jump started the car with an external battery, but after a few minutes driving the taxomether needle started to behave erratically and indicated a very high rpm. A few more minutes and the engine died. Since the battery is several years old I installed a new one and also changed out the voltage regulator (the old one gave only about 13V at 3000 rpm). Now the voltmeter reads 13.9 to 14.1V across the battery poles with the engine running at 3000 rpm, but the alternator light still shines brightly red (it is quite dim at idle).
Any suggestions?
pej
--
Per Erik Jorde

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Replace alternator naturally. It's producing amps but less than 70. (or 80 if it's an 80A alternator)
It will soon kill your new battery as well.
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Get your alternator tested... There might be a short in the winding. I have heard of this odd symptom and they usually are bad alternator..
Double check that you have installed the voltage regulator properly.
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