Thanks to Eutychius Kaimakkamis and Alberto Yagos.
Alberto, you have Andriotis’ etymological dictionary? Awesome!
The Cypriot dictionary I opened up at random confirms caracol/caracollo as the origin of karaolos, and they confirm your etymology as “twisted”. It did not say that the etymology of caracol in turn was ultimately Greek kokhlias via Vulgar Latin *cochlear, which makes karaolos a round-about Rückwanderer: caracol – Wiktionary
And who knew that the Romance words for spoon have the same derivation.
What’s this about patrolling, though? A caracole is a snail-shaped (i.e. spiral) military manoeuvre or move in dressage. Is it as generic as “patrol”?