(n.) someone who is locally admired, or sought out for their wisdom or advice by people who live nearby
Dating from the 1500s, a hamil is another word for what we’d normally call a hamlet, or a small village. A sconce is a candlestick, and in particular one fitted with a screen to protect the flame and prevent it from being blown out by the wind. (In that sense, it derives from absconsus, a Latin word meaning ‘hidden’ or ‘concealed’, which makes sconce a distant cousin of abscond.)
Put together, you have the word hamil-sconce, and old English dialect word for someone who is locally admired, or sought out for their wisdom or advice by people who live nearby. Figuratively, they are the ‘light’ that guides all the locals.
That’s an entry from the English Dialect Dictionary, which traces this word specifically to the county of Lancashire in the English northwest. “The light of the village or hamlet,” the EDD defines the word as. “The village Solomon.”