94 2.3l XLT 5 speed, 2wd

Hello. I had to replace the alternator. When it was replaced and running, the voltage at the battery was a constant 14.44v. That looked good. Then I noticed that the battery dashboard light was on. Shut the engine off, confirmed the wire harnesses were plugged in, restarted and the same thing. Voltage still running at 14.44. Turned on the a/c, blower on high and headlights. Voltage went to 14.46. Then I looked and the battery dashboard light was off and stayed off for the short time it ran. I haven't ran it any more, but am wondering if this is a bad sign?

 

The Battery light on the dash, gets 12volts from the battery with key on from ignition switch

Out at the alternator there is a light green wire on the 2 or 3 wire plug on alternator, that plug in is for the Voltage Regulator inside alternator
The green wire is the ground for the Battery light in the dash, so if alternator is not spinning its voltage is lower than 12v so battery light comes on because voltage is flowing thru the bulb to alternator

This wire also supplies "startup voltage" for alternator
An alternator can not generate voltage just by spinning it
Once its spinning it needs startup voltage so it can start to generate its own voltage, the green wire, and off it goes, now its self powering
So battery is not 12v any more its 14.4v
So battery light is now getting 14.4v thru ignition switch
And battery light ground(light green wire) is also now 14.4v........................so with equal voltage on both terminals of the bulb there is no voltage flowing thru the bulb, so its OFF

As to why Battery light stayed on, hard to say, could have been loose connection on alternator or a hiccup in new voltage regulator, should be OK but keep the receipt for new alternator

Also after driving home from work or store or ??, at least an over 10min drive, don't shut off the engine, open the hood and test battery voltage again, should be UNDER 14volts now
13.5v to 13.9v is spec
Running over 14volts long term can shorten Battery Life, or battery may already be on its way out and needs the 14.4volts all the time

After battery sits overnight test its voltage, 12.3v to 12.8volts is OK, has to have sat for longer than 6 hours for best testing
12.8v is a newer battery
12.5v is a 3 year old battery
12.3v is a 5/6 year old battery and time to shop for battery sales
12.2v or less is a failing battery