Even though I know you say the alternator has only 11.8V its worth trying a jumper cable from the alternator to the battery positive to bypass the fusible link and retesting as the connections underneath the fusible link can also go bad, as I've recently discovered.
I also don't use the factory cluster but I do have the alt light connected and if the above doesn't work then it would be failry easy to connect up a temporary 12V bulb and see if that fixes the problem.
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