Another idea, since everything is working except for the dash warning light, just put a piece of black tape over the dash light. The downside is if the alternator really does fail you won’t know it. but there may be a work-around-for that. try googling, see if there’s a circuit you can rig up using the two wires from the alternator that will turn on an led that you install on the dash somewhere. The way that circuit works I think is one of those wires is from the ignition switch, and the other is from the voltage regulator on the alternator. If the ignition switch wire is 12 volts (key in on) and the voltage regulator wire is 0 volts (engine not running) the light will turn on. if the ignition switch wire is 12 volts (key in on/run) and the voltage regulator wire is 12 volts (indicating the engine is running and the alternator is outputting voltage) the light will turn off.
It might be as simple as this
------------------------------- vvv 12 volt LED (new warning lamp)
ignition switch wire … ------->---- voltage regulator wire
Note that the dash light problem may have nothing to do w/the alternator or its wires/connectors. And it might have nothing to do w/the pcm. It could be a problem on the dash panel itself, just something shorting out making that light turn on.
BTW, if you are using the Ford 2G alternator, good idea to upgrade to the 3G version. Unlikely to be the case in a 2006, but worth checking. Ford had some reliability problems with the 2G version.