The alternator now is charging and it's light stays on until the engine start.
I was checking the wire harness that goes to the alternator and noticed a lose wire that was wrapped around it, and the only place that I thought it would go was the W terminal in the new (rebuild) alternator, but the old one didn't have this terminal, maybe the previous owner changed.
I started the car and now I don't even need tho tap the accelerator pedal to wake the alternator, and is charging around 13.75 v as soon the engine's running.
But now, the oil light stays flickering, but dimmed...
Is any relation between the alternator and the oil light?
I'm going to use the car tomorrow and see what happens.
BTW, I bought the alternator at Advance AutoParts, and while I was there I got 5 qt of Mobil 1 TD 5w40 oil and a Mobil 1 oil filter for $29.99 (+ tax) that was on sale, I thought is a good deal, that's why I'm telling you, if somebody is interested.
Thanks for your help and attention!