This is an instance of etymology ex antonymo. There is no semantic relationship between "light" and "to lead". But the antonym, skotos "darkness", is derived by Herodian from skhethō "to hold back" (see σκότος / σχέθω), because darkness is what holds us back from moving forward. Accordingly, since augē "light" is the antonym of skotos "darkness", it must have its etymology in the antonym of skhethō. The latter means "to hold back", and its opposite is "to move" or "to set in motion", hence agō which is formally close to augē and semantically connected with "to move". In that case, the etymology σκότος / σχέθω came clearly first, since it is better designed both formally and semantically (incidentally, it is also attested first as it goes back to Herodian). That αὐγή / ἄγω is modelled after it is explicit in Etym. Gudianum and Etym. Magnum where there is a connecting particle (see Parallels). The requested formal manipulation (adding a [u]) is not mentioned