At idle the alternator only puts out about half its max rating. This sounds lousy, but it’s much much better than the old, pre-1964 generators which would put out absolutely nothing at idle.
So if your load is more than half the alternator max rating, the difference is going to come out of the battery. If the battery is getting old or the cables or connections to it are corroded, the battery voltage will droop a bunch. How much is too much? A little droop is normal, maybe up to half a volt or so. More than that is tolerable, but you will notice the lights and fan sagging a bit.
The problem still could be in the alternator, if it never puts out enough to charge the battery fully, even a good battery will exhibit these symptoms. So it’s still not clear what is the prob.
I would first check the connections. Most are corroded and can benefit from a wire brushing of the terminals and inside of the connectors.
Then run a battery test. First charge the battery up fully with a guaranteed source of charge, the alternator doesn’t qualify as it’s an unknown right now. So charge it up with a battery charger overnight. In the morning remove the charger and turn on the headlights. A good battery will run the headlights nice and bright for at least 15 minutes to an hour. A weak battery will start dimming the lights after 10 minutes or even less. If the lights start getting yellow in under 20 minutes I would consider the battery weak and look for a replacement.
If the battery checks out okay, then the dimming is not caused by the battery, but may be a problem with the alternator. It might have a loose belt, so it never spins quite fast enough, or it may be never be putting out enough to charge the battery fully, or it may be set to cut off charging at too low a voltage, or maybe it’s temperature compensator isn’t working. Complicated isn’t it?
Good luck figuring this out. The above hints are a start and should help.