Hey! Thanks for accepting me, this is my first post.
Keep in my English is not my mother tongue please, I'll try my best.

I have a Civic 98 D16y9 (I'm from Venezuela) and I'm having an issue with my Battery/Alternator. Long story short, I took the dashboard to change the oil pressure bulb, and battery bulb, since they were burned. At the moment of starting the car, the lights come up normally, but when the car turns on, the battery light stays on (oil pressure working perfectly), if I turn the AC on, then the light is even brighter. I bought the car a few months ago and I think that the light has always been turned on, but since I didn't change the bulb at the correct time, I didn't notice, my bad.

The battery is charging fine, 14.2 volts constantly on the battery, but I noticed that the lights flicker a little.
In my ignorance I thought that my alternator was going bad, I thought that the voltage was OK but the Amp was not, so I took the alternator off the car and bought another one.
When buying the new alternator I noticed that it's a 5th gen civic alternator that my car has, not a 6th gen. Here in Venezuela, they are almost the same thing, just that the 5th gen has a round connector and the 6th gen a square one. Since the conversion was already made on my civic, I bought the 5th gen alternator and plug it into my car.

The car was doing exactly the same, the light turns on when passing the key, but when turning the car on, the light was still on.
The new alternator is checked, charging fine the battery at 14.2 volts.

Then I thought they (the old owner) maybe wired wrong the connector to the 5-gen alternator, so I disconnected the cables from the connector and tried to rewire myself.

My car has 3 cables going to the alternator:

White/Blue = L signal = Charge light
Black/Yellow = IG Power
White/Red = FR Signal

According to a friend that works with Honda cars here, those are the only wires my car should have, so it is safe to assume that I don't have any other cable missing. (I can't take the car to his workshop, it's very very far away from where I am)

New alternator came with this

So I rewired the connector following that, but now I'm having another issue. The battery light on the dashboard is not turning on when I put the key in the second position.
The battery is charging, but I'm pretty sure something is bad on there because if I take the white/blue cable and I ground it to the chassis, the light turns on.

Things to know:

My ECU is a p2k-v51 It's not the same as p2k-01, I have tested the signals from the ECU to the alternator and they are fine, the 3 cables receive a signal, but I'm not sure what are those because it's impossible to find a diagram for my ECU.