Where does “dyer” come from?

I can't write this etymology summary because the chain provided only contains cyclical repetitions of "English dye" and "English die" without any older language sources, a cognate root, or etymological depth. A valid etymology requires tracing back to an actual origin language (Old English, Proto-Germanic, etc.) with documented forms and meanings. To write an accurate one-sentence summary, I would need a chain that shows the actual historical progression—for example, something like: English dyer | Middle English dieren | Old English deagere | Proto-Germanic *daugijanaz. Could you provide the complete etymological chain for "dyer"?

dyer (English): One who dyes, especially one who dyes cloth etc....