Naruto Shippuuden Episode 12

[Assertn]

Yeah, Gai wouldn't fall for Itachi's Tsukuyomi that easily. He's had years of training against a skilled sharingan user. He would just look at Itachi's feet.

In fact, I'd say that Itachi would have a harder time fighting a taijutsu user than anyone else. Remember from Sasuke's fight with Lee, the sharingan won't help you if your body can't move as fast as your eyes can anticipate. While Itachi might be faster at performing Ninjutsu, he definitely won't be faster in pure agility and taijutsu.