TBM not trying to muddy the waters further but I did have a similar issue on my narrowboat driving a high current alternator. The weight of keys on the ignition switch had turned it off. The alternator then started charging intermittently and given it's size (160 amp) I could hear the change of load on the vintage diesel driving it. There was a random cycle lasting a minute or two before it would cut back in again. The warning light followed this sequence as expected.
Point I'm making is the randomness of your issue could be down to intermittent and/or resistive feed from ignition switch to warning similar to my accidentally turned off ignition switch, the results of which are unpredictable as alternator appears to self energise for while then drop out again with sequence repeating.
Suggest therefore following up on your suspicions of this feed to warning light or just jury rigging a cable from live side of battery to warning light, remember to remove it though when you want engine to stop though. As your findings develop I'm more inclined to think this may be the issue rather than a failed diode. The ignition switch side of warning light feed receiving a varying voltage directly affecting its degree of illumination as the alternator maintains a more constant higher voltage to battery and other side of warning light. This would explain why it's brighter when you add load such as wipers as ignition side of warning light gets an even lower voltage.
