Battery Light Issues Replaced Alternator & Battery

[Saree]

Hello I am hoping someone here might have an answer. We replaced the alternator and battery in my 1998 expedition. When I start it up the battery light is still on. The car will die if left running when battery juice is gone and would have to recharge battery if we wanted to start it again. (If car is not running and just sitting battery is not drained which for me ruled out a short or something running while car is off, locked, and we are not in it) Nevertheless, the battery was tested, and is good, new alternator was removed and tested and that too is good. When measured on the vehicle the alternator is putting out 11.8 amps, which means something is stopping it from working but the alternator itself is not bad, I replaced it twice and this is the same issue. I was told it could be a wire coming from the alternator and was going to replace the pigtail until I found out that if I replace it, that is simply the plug and not the entire wire. If there is a problem in that wire and it is not simply the part that plugs in that is wasted money. I am also unable to get a complete wiring harness from an auto part store. Could this be as simple as a fuse? I am at a loss here and already spend hundreds of dollars. I do not know where to go with this now, but had a feeling it was something small that I just didn't notice or think of.