'intact-brained' originates from Modern English as a compound of 'intact' and 'brained'. 'intact' ultimately comes from Latin 'intactus', where 'in-' meant 'not' and 'tangere'/'tactus' related to 'to touch'. 'brain' comes from Old English 'brægen'.

'intact' passed into English via Latin 'intactus' (and French influence) to mean 'untouched' or 'unharmed' in early modern English; 'brain' developed from Old English 'brægen' to the Modern English 'brain'. The compounded adjective 'intact-brained' is a more recent English formation (modern/colloquial usage) combining these elements.

Initially, 'intact' meant 'untouched' and 'brain' referred to the organ; over time the compound came to mean 'having an undamaged brain' and figuratively 'mentally sound' in modern usage.