With the new info, it sure sounds to me like you have a problem.
I would bypass the fan switch and force the fan on and turn anything else on to create as much of an load as possible. Then hold the engine at 4,000 RPM or so to simulate running down the road. Then check for voltage drop across all the connectors dealing with the charging system. Also check battery voltage with a DVOM and compare with your meter.
Also check AC voltage on each leg of the stator (especially if you start seeing the low voltage problem). It does not happen often, but a shorted stator can be just fine at idle, but voltage will drop at higher RPMs and/or when it's hot. Check both with no load (regulator unplugged) and under load.
Most of the time when a 3 phase stator starts to die, only a single phase goes, so if you compare the 3 and see one that has lower voltage, then you found your problem.
I am placing more bets on a bad connection. That brown connection is known for having problems.