Old English wull, from Proto-Germanic *wulno (cf. Old Norse ull, Old Frisian wolle, Middle Dutch wolle, Dutch wol, Old High German wolla, German wolle, Gothic wulla), from PIE *wele- (cf. Sanskrit urna; Avestan varena; Greek lenos "wool;" Latin lana "wool," vellus "fleece;" Old Church Slavonic vluna, Russian vulna, Lithuanian vilna "wool;" Middle Irish olann, Welsh gwlan "wool"). Figurative expression pull the wool over (someone's) eyes is recorded from 1839, American English.
Thoroughgoing or complete: “The door-to-door salespeople are wasting their time with Evans; he's a dyed-in-the-wool advocate of shopping on the Internet.”