1974 1.8L not holding a charge, Causes other than alternator Options

[Robnxious]

I have tried digging in on this a bit on here searching, and have seen posts saying "make sure it's the alternator before replacing". Here is what I have found so far. When the battery has a full charge, the volt reading is 12.75, and when it's running, it's about 13.5 (I remember reading on here last night that the running voltage should be about 14.5 IIRC). Which tells me it SHOULD be the alternator (that and the fact that if I run it with lights on at night, it needs charging when I get home). Also, my battery charger has an alternator check function and it said it was bad.

But, I also did the old shade tree mechanic trick of disconnecting the negative battery connection when the car was running, and it didn't miss a beat, still idled strong.

I do have an alternator that I bought (yeah I know, didn't see the threads saying "make sure it's the alternator before buying" until after I had ordered it), but seeing how this is a PITA job the first time, I am hoping I can get my new baby up and running easily.

Any help is appreciated, and thanks in advance