That will be the blue wire and won't be causing this problem that stops it from charging and is common on most Fords, I would personally say your battery is dead.

The reason the alt could be glowing is when it tries to charge the battery it's shorting through it and so causing the alternator to glow which is not good!

If you do disconnect the red wire from alt as said firstly MAKE SURE you disconnect the black battery earth lead first (Negative) AND TAPE up the connector on the red wire at the alt and make sure it does not come into contact with any metal, although personally I don't think alt has anything to do with it.

Martin