You will need to check voltage again after engine has been running at least 5min
Should drop to below 14volts
If it doesn't then voltage regulator in the new alternator has failed
Over 14v for extended period will ruin a 12v battery, cooks it
2008 2.3l Ranger will have a 2 wire plugin for alternator's voltage regulator(V6 engines use 3 wire)
Red wire should show battery voltage key off or key on <<< check this
Grey wire is the Battery Light wire, it should have 12volts but only when key is on.
It provides Startup voltage to get alternator working <<< check this
Battery light bulb gets 12v from fuse #9 in cab fuse box, and that passes thru the bulb and comes out at the grey wire on alternator, when alternator is not spinning it is, in essence, a Ground, a lower voltage, so with 12v on one wire and low volt(ground) on the other the Battery Light Bulb comes on.
After startup the alternator generates its own voltage and that voltage is fed back to the Grey wire thru diodes in the voltage regulator.
So grey wire would have 14.8v(in this example) and battery light bulb would also have 14.8v from fuse #9, if both connections on a light bulb have the same voltage then bulb is OFF, no current/electrons are flowing thru it to heat it up.
So your grey wire is not getting alternator voltage after start up, which would be a voltage regulator issue
This is not uncommon, but the more common issue for battery light being on after startup is alternator output dropping below Battery voltage, in this example 12.4v, so if battery light bulb has 12.4v from fuse #9 and under that from grey wire on alternator the battery light would have electrons flowing through it so would heat up and glow, the lower the voltage the brighter the bulb, flickering would be up and down lower voltage coming from alternators grey wire
Now the grey wire could be shorted to ground in the harness, worth having a look, but I wouldn't expect the alternator to start working if it didn't get the 12v FROM the grey wire to start generating voltage
So test Grey wire voltage(key ON) when its unplugged from alternator, should read Battery Voltage(12.4v) if wire is OK, if its less then there could be a short
An alternator is similar to an electric motor, the voltage regulator controls the voltage to the brushes on the rotor, if you don't shut off voltage to the rotor then alternator would drain the battery when engine was off, it would try to spin the engine via fan belt, lol.
But if you don't have voltage on the rotor then alternator will never start to generate its own voltage, thats the purpose of the Grey wire, Battery light is a bonus.
Grey wire gives voltage regulator 12v for the rotor so alternator can start up
Fuse #9 voltage is cut when key is off so when you shut off the engine, alternator's regulator has no voltage from alternator or grey wire so no draining the battery