Thanks to all of you, I was able to test the alternator and verify that it's working properly. In order to make tests at the battery I had to drop it out of the frame, which is difficult because it's mounted underneath.

I found that the voltage at the battery posts was correct at 12.6, but at the starter was only ~7.1v. To make a long (and embarrassing) story short, when I installed the battery earlier, I must have knocked the positive terminal loose. As soon as I reset and tightened it, all was well again, 14v+ at the terminals while charging, no flickering, and very little voltage drop when I turn on the lights.

So, I guess my mechanical skills are on full display here. My only defense is that mounting the battery is difficult because of the close space and awkward access. Had it not been for the thorough diagnosis all of you provided, I might have just bought a new alternator.

Again, many thanks for your quick replies and support.