Diagnosing an Alternator or Voltage Regulator

Hello, I'm having issues with my 1983 Plymouth Scamp GT.
Had the battery die, got a jump and it worked. Died again, jumped again, battery tested at 9% power, replaced battery. During the second round of dying, the lights stopped working, and tachometer was reading at least 1k rpm low.

Since the battery was replaced, it died two-three days later.
I have had it on an overnight trickle, seems to be resting at about 12.7 volts. A reading with the car running at 1500 or 1000 rpm is 12.66. With the lights on, it is 12.4 and slowly dropping.

My guess is the alternator. I looked for parasitic drains first, but had no amp draw (or .02, something small) so that was ruled out. A new alternator is only about $40-50, so I'd love to avoid the shop diagnostic fee and installation fees.

Belts are tight, though the alternator itself has a shitty mounting system and tends to travel 1/2" loose on the screw over time, with its high quality tattered plastic bushing. After tightening, the problem remains.

Any ideas what to check next, or does this sound right?