Battery not charging but alternator shows 13.5v

[Eric0]

Hi everyone! 

I have had battery charging issues before which have been resolved using this wonderful forum and well... here I am again! Yay...

So, from the beginning. I've been driving my car for about 2 months now and my dash-lights went out about a week ago. Then yesterday, I'm leaving school and the car decides it doesn't have enough charge to start. I replaced my battery thinking it was just old (4 years) and got a nice fresh yellow-top. That made me curious to look at my voltage gauge and it displayed 13.88v. As I drove the car, I noticed it dropped to 12.88 and stayed there.

When the car is off: battery is 12.42v.

When the car is on, battery is 12.42v.

When the car is on the road, 12v-12.88v.

I have driven the car for about 3 days and its consistently sitting around 12v-12.88 but doesn't go up to 14v. My voltage gauge shows 12.88v max voltage when driving. 

I checked the alternator stud and it showed 13.53.v charge. I checked the 75A fuse, and it showed 13.48v. I started the car and disconnected the terminals from the battery to measure the charge to the battery and it read 12.41v (I did this quickly as I know the battery acts as a buffer). So, the battery is being charged at 12.41v, the alternator is producing 13.53 volts, all fuses are good, I don't have a charge light but my dash board lights did go out before I started noticing this problem. 

I tested the exciter wire (off the alternator) when the car is off: 0v, when the car is on: 0v (red/white wire off alternator)

I tested the big wire (off the alternator) when the car is on: 0v, when the car is on: 0v (big white wire off the connection)

The way I tested the wires was by taking off the plug and measuring the pins while the car is running off the alternator.

I replaced the alternator in 2020, so I believe it should be good. But I do have an oem sitting around that was tested good before.

Do you guys have any suggestions?