Battery Light On- New Bat/Terminals
 

First and foremost, thanks for taking the time to check this thread.
1997 Camry 2.2 155k Miles

I bought the car a few months ago and had intermittent starting issues due to the terminals having massive corrosion. Eventually it wouldn't start, regardless of a jump, or battery charge. So replaced the battery and terminals a few weeks ago. I couldn't source an OEM fusible links terminal set in time, so I replaced it with a battery cable repair/ splice kit. (Part 08864 on oreilly parts website).
The car started right up, but fast forward a few weeks and the battery light is on. I brought it to auto zone for an alternator check, and they said it's bad. I'm not sure whether or not it's actually the alternator, or a potential bad wiring job? I only saw the 2 main large gauge cables connected to the battery, so I only reconnected them. The wire on the splice kit with the yellow nut on it is still just hanging there... did I miss something? Am i supposed to wire that somewhere? Or is the alt simply bad? Connections look good on alt... fuse looks good, and it didn't seem to have an issue until I replaced this stuff. Maybe it was there all along but the terminals masked it? Sorry for the novel here, but I've tried finding answers to no avail.
Edit- battery voltage was 12.08 on bat test as of today, and have been using a/c etc last few weeks

The cable could be a universal fit and have an extra lead.

Check voltage between white wire at alt connection plug and ground at 2000 rpm. Should be 13.9-15.1v.

Check AM1, AM2, ALT-S, IGN, ALT, Gauge fuses.

Thanks Toyo-
I only checked voltage at battery, and AutoZone said they could bench test it if I removed it.. and I only checked the alt fuse. I'll check everything tomorrow n get back to you. How would I go about checking the wire at the connection plug?

Connect volt meter between white wire at alt harness plug and ground.

Alt harness plug, plugs into alt.