Where does “g·ilèt” come from?

g·ilèt (Franco-Provençal) comes from French gilet, from Italian giulecco, from Turkish yelek, from Ottoman Turkish یلك, from Old Anatolian Turkish يَلَك, from Old Anatolian Turkish يَل, from Old Turkic 𐰘𐰠, from Proto-Turkic yẹl — wind.

g·ilèt (Franco-Provençal): vest