agog: [15] Agog probably comes from Old French gogue ‘merriment’. It was used in the phrase en gogue, meaning ‘enjoying oneself’ (Randle Cotgrave, in his Dictionarie of the French and English tongues 1611, defines estre en ses gogues as ‘to be frolicke, lustie, lively, wanton, gamesome, all-a-hoit, in a pleasant humour; in a veine of mirth, or in a merrie mood’), and this was rendered into English as agog, with the substitution of the prefix a- (as in asleep) for en and the meaning toned down a bit to ‘eager’.
It is not clear where gogue came from (it may perhaps be imitative of noisy merrymaking), but later in its career it seems to have metamorphosed into go-go, either through reduplication of its first syllable (gogue had two syllables) or through assimilation of the second syllable to the first: hence the French phrase à go-go ‘joyfully’, and hence too English go-go dancers.
"in a state of desire; in a state of imagination; heated with the notion of some enjoyment; longing" [Johnson], c. 1400, perhaps from Old French en gogues "in jest, good humor, joyfulness," from gogue "fun," which is of unknown origin.