hi, my name is XXXXX XXXXX I will try to help you .
the charging voltage looks good and you did check the connections at the alt ,so at this point if this was my vehicle ,I would take off the alternator and run it to a parts store and have them check it before you buy an alt.
as a note: the voltage regulator is most likely the issue as far as the charging light is concerned.
it will still charge its just the circuit to the light ...jazzmaster...
you might want to get this checked, at most auto parts stores they will do this for free.
it could be that the alternator is bad ,even though you put a new regulator ,it may have a bad diode in it and a good tester machine will tell if that is the issue. the voltage looks ok,it should show a little higher, around 14.5-14.8 .