+1 ^^^^
The Battery Light means alternator voltage is LESS than battery voltage which is a bad thing in that you are powering the vehicle using your new battery which will cause it to drain and it would no longer start the engine
The battery in any vehicle is ONLY used to start the engine, thats its only purpose, after start up the alternator powers all electrics
Key OFF, a new battery will show 12.8-13.0 volts DC
3 year old battery 12.5volt
5/6 year old battery 12.3volts, and time to shop for battery sale
12.2volts or less is a failing battery
Yes, after startup voltage AT the battery should be 14-14.8volts DC, that "fast recharge voltage"
After a few minutes it will drop to 13.5-13.8volts, and stay there as long as engine is running regardless of lights or heater fan speed
If you see under 13.0volts AT battery with engine running then alternator is not working, Battery Light confirms that
Why did you get a new battery?
Alternator wiring test;
Use alternator case for ground
Key OFF
B+ wire, larger wire on back of alternator, leave it connected for test, should show Battery voltage, so test battery first
Unplug the Voltage regulator 3 wire connector, yes its inside alternator
Test Yellow wire should show Battery voltage, if not ALT Fuse is blown in engine fuse box
Test light green wire, should be 0 volts
Turn key on, should now be Battery voltage, this is the Battery Light wire
If wires test OK then replace alternator, you can just replace voltage regulator but.................its been my experience that it will only last a few months before another issue pops up like a loose bearing