On my 1994 525iT
Almost every time I turn on the A/C, I get a F/FOG LIGHT + LOW BEAM warning on the CCM.

While this is happening:
The left turn indicator on the instrument cluster is partially illuminated
The dashboard does not click when the turn signal is on
The left high beam headlight is partially illuminated (even when headlights are off) and switches off and on, alternating with the left turn signal

These problems go away when the A/C is off.

Things I have done to remedy (basically everything that I have found in posts and that is common sense):
New LKM
Cleaned and checked all connections
Changed bulbs
New voltage regulator for alternator

Could it be the alternator itself?