Long post, interesting story that probably won't help you at all
You won't believe what I found when I bought my first ever Golf GTI Mk1 that had exactly the same problem.
I changed the battery, nil fix. I confirmed that I had an output from the alternator. Did loads of other things and was at my wits end and had resorted to carrying around the old battery and jump leads.
Did this for about a month and then one day I was dotting around the engine bay with a multimeter on something like the 5V scale. I touched one probe on the case of the alternator and the other on the rocker box cover (don't ask me why, but it turned out to be a good idea), it read 2V
Checked the earth strap between alternator case and engine, looked OK, so took it apart. Turned out to be a plastic washer installed under the strap
Chucked the washer away and never had a problem again
Turned out, the guy who owned the car before had spent a fortune at the repairers trying to get that one fixed, he gave up and flogged the car to me. He was gutted when he found out what it was.........and very suspicious as to where the washer came from as he didn't put it there.