Gale is most likely a variant of the word Kelt and all its dialectical forms: Celt, Gaelic, Wales, Kale. G and K sounds are both glottal stops which interchange easily between dialects. Furthermore, there is a tendency in Indoeuropean languages for G to become W between the different codes of Indoeuropean; hence, Wales in English becomes Gales in Spanish and War in English is Guerra in Spanish and Win in English is Gan-ar in Spanish. Galipoli in Turkey was the city of the Gales (Gauls, Kelts, Wallaces, Gillis). Galicia in Spain was another stronghold of the Gales. The Gales/Gauls were one of the great tribes of Europe; however, today they only have one small independent country for themselves, Ireland.
Spelled "Gale", is simply an English synonym for "wind storm". But my research shows that "Gayle" is derived from the Old English spelling for "gaily", meaning "happy", as is the spelling "Gail". Spelled "Gael", it refers to the Gaels, who were originally an Irish tribe who have subsequently spread to Scotland and the Isle of Man, and appear to be the originators of the Gaelic language.