i think that since via verse equiv genjutsu is similar to telepathy/illusions gowther wont be affected by them in the slightest,
tsukuyomi also wont bring anthing since gowther is essentially a doll, no emotions therefore "breaking his will" is rather difficult
itachi only has his normal taijutsu (which will lead to gowthers win since he can survive having his head punched off), normal ninjutsu and MS-techniques, itachis ninjutsu never shwoed real strength, at least not to the point where it is understandable to assume that they would work on gowther,
only MS-techs, like i said, tsukuyomi wont bring anything excpt causing itachi to lose a hugh amount of his chakra, amaterasu and susanoo are the only options, unfortunatly amatersu is dodge-able and susanoo has limited range, plus itachi is ou of chakra really really fast,
on the other hand gowther only needs to use blackout of itachi will be unconscious for 10 minutes, and its range is 3 miles that means that gowther can activate it from a distance which itachi cant reach with totsuka
85 from 100 fights go to gowther ^_^