If the field circuit goes open, you lose regulation. Alt will put out increasing voltage as RPMs go up. The light will glow if alt voltage goes high enough *above* the battery voltage, as well as if it goes below.

On a Bosch alternator, it's the wire hooked to the spade terminal. There's a second spade terminal inside the alt. I've had the wire come loose inside.

I don't understand how the light could glow without you seeing the problem on your voltmeter, whether or not you have the failure I'm describing.