I have not deeply researched Quakers, but always found them interesting.
As far as the term, "Inward Light", I would opine that combines the idea that heaven is within you, and receiving heavenly guidance. So, when you listen to or follow the "Inward Light" (via intuition I guess), that would mean that through prayer and yearning, you discern what God wants for your life. Why they use the term "Light" is because it illuminates. That's my best guess about how your great grandparents may have seen it.
I have little doubt that the "Inward Light" is just as you describe. It's something that I have known my whole life and live by day to day but don't realize it because I just do.
I guess, to me, everyone has their own "Inner Light" as well. In a time and era where the light of a fire meant life or death, quenching another person's light was a death sentence.
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