Rush lights got their name from the stiff, reedy, water plants that could be used as primitive candles. Rushes have an outer bark, but are soft, absorbent and fibrous inside. The rushes would absorb melted fat or oil, and could then be lit. A cheap, readily available source of light.
Now making one would just depend on the availability of rushes near you, and your patience. From The Natural History and Antiquities of Selbourne, "The proper species is the common soft rush, found in most pastures by the sides of streams, and under hedges. Decayed labourers, women, and children, gather these rushes late in summer; as soon as they are cut, they must be flung into water, and kept there, otherwise they will dry and shrink, and the peel will not run."
So, evidently, mature rush stalks are ready in late summer or fall. You then need to peel off most of the bark, leaving an intact strip along the length to hold it up straight. Leave the soft pith attached to the bark and let it dry. Once it's dried, dip it in melted fat or oil (you could use melted tallow, olive oil, or even liquid paraffin.) Dipping several times seems to help the candle last longer, as does adding a bit of beeswax to the fat/oil.
Rushlights were usually held up/suspended by a "rushlight holder" or clip. They're likely to smoke and drip, so you want to be careful how you burn them.
Let me know how it turns out. Making your own rush light (for me at least) would rank up there with making lye from wood ashes. One of those things that are interesting to know about, that make you appreciate how easy we really have things in our modern world, that might be fun to try once just to say you've done it...but that I wouldn't "rush" out to do every day.
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