It depends on how mechanically inclined you are. I took one off of
a 95 in a junkyard in about 8 minutes. It went back on my 89 in 25, but
I had to change the terminals to fit the new alt.

Mike,  Symptoms are dimming lights at night and battery gauge dropping
while the engine's running from it's normal position.

With a voltmeter check across to + and - terminals of the battery for
14 VDC, or slightly more with the engine ideling, accessories off.  12
VDC or less is unacceptable.  Raise engine speed to ~ 2000 RPM and
re-check voltage, if still less than 14 VDC replace alt.  If voltage is
correct, replace voltage regulator.
Check electrolite level in battery, if not a dry cell...low mtce., not
NO mtce.

Replacement is simply removal of the battery cables, belt, four bolts
and the connector and then reverse the procedure using correctly sized
hand tools.  Should take less than an hour overall.

bradtx

Alternator on any of the Mustang motors in '99 is pretty easy. The unit
sits right up top-front on the motor. Hand tools only plus something
with a half inch square drive (ratchet) to operate the belt tensioner.
Check the belt while your at it since you have to handle it anyway.

A generator/alternator that is degrading tends to cause the electrical
system to behave weird (lights dimming significantly, lights
flickering, etc.). The most common symptom of a bad one is that the
battery loses its charge. There are battery/alternator testers that can
check it in the car although they are not 100 percent accurate.

Dan
2003 Cobra convertible
With some stuff and things

A lot of shops will test it for you for free and will be able to tell.