Nothing normal about that. The light should be off when the engine is running. A soft glow (only visible at night) at idle is OK, but "gradually will get a brighter red with more rpm" is a sign that the alternator-regulator aren't charging.
really does sound like a failure of the alternator's regulator. At 4000 rpm it should put out 13.7 to 14.5 volts. climbing to just 10 volts means it is missing ⅓ of its output, typical of a diode failure.