Cheap, wood-handled large paintbrushes are a great source of tapered wood for masts!
I bought a pack of 12 brushes from "The Works" discount bookshop for £2.99. These have wooden handles about 25cm long. The larger ones are too thick for masts (in any scale) but the medium + small ones should all be usable. Saw the handle off just above the point where it "bulges" slightly, then sand it down to get rid of the varnish + printed manufacturer's name. As a bonus, there should be enough of the handle left on the brush to use it - these particular brushes are far too coarse for painting models but are fine for applying glue + sealant, and the smaller ones are good for drybrushing + weathering.
Here's a photo of a 1/96 1900s steam trawler I'm working on (static model, "kitbashed" from a part-built second-hand wooden kit), both masts (missing from the kit) were made using brush handles. The finished items will have metal rigging fittings and will be painted the same colour as the superstructure.