Probably not the rotor or stator as they rarely fail, and should be "bad" all the time if they do.
Probably not brushes because as they wear, output (current) drops but should still increase with RPM.
Probably not (power/stator) diodes - just 'cos it ain't.
So, faulty regulator, or a bad connection?
Ensure that your charge lamp is operating.
Does it extinguish at idle?
Does it come on after the volts drop above 2,000RPM?
(If not, I'd suspect the regulator)
With ignition-on before starting, do other dash lamps come on that then extinguish with the charge lamp (eg - warnings like fuel, engine overtemp, brake - but NOT handbrake, oil pressure, seat-belt)?
(Reason - these usually parallel the charge lamp so that charging initiates and continues - in case the charge lamp loses connection or blows.)
Otherwise I strongly suspect a bad connection - increasing RPM vibrates the bad connection or pulls apart the cable/connector break etc.
The following should be done in order of easiest first, maybe testing after each (or a few) steps.
Unplug, inspect & replug its connector.
Maybe also its heavy (B+) cable to the battery AFTER disconnecting all battery grounds (negative terminal) - but maybe wait with this till last to avoid clock resets etc.
Do a similar unplug, inspect & reconnect for any alt (heavy) to battery connectors or fuses, and regulator fuses (in the main fusebox - any other dead circuits? - the alt/reg fuse is often with dash meters etc but could be elsewhere).
Wherever possible, rotate fuses (of the same rating). That does the same break/remake connection, and transfers any fuse problems to another circuit.
During idle, does the jiggling of any related cable kill the alternator output?
Above 2kRPM, does jiggling restore charging?
(Please - I refer to jiggling of cables etc only. Please
do NOT lose fingers, hands, arms, torso etc to fan belts, fans or another moving part, nor burn the same on hot exhausts etc. Reconsider the last sentence if you at any stage were considering jiggling anything other than the cables involved.)
Save this for near-last with engine off does tapping the back of the alternator with a hammer fix anything? (I'm serious - but not too hard - it's just to give it a bit of non-electrical shock treatment.)
Do you have any non-standard voltage sensing circuits fitted?
If the above yield nothing, unless anyone else has a simple solution or suggestion, I'd suggest either a pro check it, else replace the complete alternator (ie, with a second-hand unit).
It could be anything from worn brush holders, insulation breakdown, broken windings, regulator breakdown, etc.