Thanks for the tips. I have just secured a good deal on a 3rd-party power adapter, and should have it in hand this coming week.
Indeed. There is almost certainly a 3rd circuit in there somewhere that handles the bi-color LED for the charge indicator.
Hopefully by this time next week, I will have all the parts together and the iBook repaired. The battery seems to be in decent shape. It did successfully charge and support the iBook for over an hour of time.