My car had trouble starting...found out the battery was almost dead, and it was old. So I replaced it with a new one. about a month or so later I started to see my headlights Pulse, but not only them but also the interior lights.

Sometimes it does it when I'm stopped, and others when I'm on the road doing 45ish and even highway speeds 65+( all kinds of RPM's )

It doesn't happen all the time, but it is most of the time.

Also I think this might have to do with the car idling rough here and there when I come to stops. if you give it gas to make the RPM's go to 900-1200 it stops.

 

your alternator is dying. classic signs. your alternator is not putting out enough amps to recharge your battery even if you are driving. the pulsing gets worse the more load you put on the battery and alternator.

 

What would be the better option...to rebuild it or just buy a new one.

 

I always have an auto electric shop rebuild my alternators. That way you get the same unit you gave them.

I've had bad luck with several rebuilds from parts stores...

+++++++++

PS, make sure the battery clamps are tight before you mess with the alternator. Often, new batteries have smaller terminals, so even with the clamps tightened as far as they will go, they can still be turned...