Was the negative cables replaced along with the positive? Many people seem to skip that one. If battery and alternator check out, it has got to be a cable or bad connector somewhere. If the light is intermittent, it could still be the alternator acting up in certain RPM ranges.

I have never heard of a bad sensor causing this. It is possible, but I cannot find an instance of this from Googling.

I have never heard of a sensor causing this. Possible, just never heard of it.

Have your alternator tested for you. 99% certain your alternator has failed. Most auto parts stores will test it for free and it takes just a few minutes.

A bad alternator can kill a battery, and vice versa.

What car?

A battery can go dead because it isn't being charged. That probably is what the lught is showing, that the alternator is not charging.

You have a bad alternator.