I just ordered an internally regulated 1 wire alternator to clean up this mess under my hood. When removing the external regulator, what is this and should it go also? Also, any idea which of these wires runs to the "idiot light" on my gauge cluster?
That looks like the radio noise suppressor, to help keep alternator noise (whine) out of the radio. The idiot light connects to the "I" terminal, which also provides the exciter circuit for the alternator.
Most of the delco remy 10si (or clone) one wire alternators have a suppressor built in. You should be fine as long as the alternator you purchased has one.