I agree with almost everyone...the belt could be slipping, or the batteries may be fully charged. And you could have a charging problem.
Now for my SWAG....
Operating the coach with a faulty belt-driven alternator isn't going to hurt the bus. It could reduce you to walking however....if ignored over long periods, if the batteries wouldn't restart the bus after a shutdown.
The not-gen light will come on if there's no load on the electrical system and the batteries are fully charged. Turning on any voltage hungry source should shut the light off if that's your situation. If the light goes off with a load, and the system maintains 26Vdc plus, you don't have a problem.
if the light stays on with a load on the batteries, you may have a bad relay? You can check the battery voltage with a dig voltmeter. If the voltmeter reads 26-28Vdc, you don't have a problem.
It the voltmeter reads less than 25Vdc, something's not right. Then we get to start new SWAGS!
In a bus' designed function, it's rare that there's no load at all on the electrical system. AC or heat is almost always on...or both. Big loads all.
One other item, which you haven't mentioned is that if any charging device such as a genset is running and charging your batteries, the not-gen light will light up.
Any time the regulator senses fully charged batteries, the alternator may quit charging.
Craig brings up an interesting point with the light locations. He explained how to verify the air switch that controls the alt relay.
It's possible that it's air pressure related (as Dr. Dave sez). The relay is in the rear junction box.