Okay, I think I covered everything here. If Kishomoto ever tells me otherwise,
my eyes will be the ones bleeding.
Why Sasuke Does Not Have the Tsukuyomi
What Sasuke uses is the common Sharingan Genjutsu but chanelled through his Mangekyou Sharingan which apparently has the effect of amplifying its strength, rendering him capable of instantly incapacitating powerful opponents.
Sasuke casts the genjutsu with one eye of his Mangekyou like how Itachi's casts Tsukuyomi with his left eye. But whilst Sasuke typically casts it
with his right eye, he has also done it with
his left.
Twice, since he appears to be holding his left eye in pain. And even regular Sharingan Genjutsu can be used through a single eye as demonstrated by
Madara and
Itachi. Itachi even uses
Sharingan Genjutsu with the Mangekyou himself as his Tsukuyomi is cast with his left eye, not his right.
Madara has done the same.
Sasuke has never once called his genjutsu, Tsukuyomi. Kagutsuchi was named the second time it was revealed but it was still revealed and, unlike Tsukuyomi, was an ability Sasuke and the reader had never seen before. Both
Danzo and
Tobi compare it to Itachi's Tsukuyomi - understable since they are brothers and both use Amaterasu and Susanoo - but neither of them actually call it Tsukuyomi. Only twice has Sasuke used the genjutsu with a name which was
"Sharingan" and
"Genjutsu - Sharingan" respectively (just like
Madara). The latter occasion also makes it explicit by showing his genjutsu side-by-side with Itachi's Tsukuyomi.
Tobi implied that Sasuke had received
Itachi's eye techniques but Itachi had only sealed a single use of the Amaterasu inside Sasuke with the
Transcription Seal: Amaterasu which Sasuke had no actual control over. And when that was used his eye
transformed into Itachi's Mangekyou Sharingan temporarily. So if Sasuke used a Tsukuyomi from Itachi, his eyes would have changed to show it.
The genjutsu Sasuke uses against B resembles the Tsukuyomi with its
inverted colours but this is also the only time that happens. Every other time when we see the genjutsu itself, it doesn't have that visual effect. It's also said by Itachi and the second databook that the Tsukuyomi can only be broken by an elite Uchiha with the Sharingan which we later saw proven and explained. Yet B was essentially freed with just a genjutsu dispel.
Ultimately, Sasuke only has Amaterasu and Kagutsuchi with Mangekyou. Amaterasu was first used with his left eye
against Killer B. Kagutsuchi was used and named against the Raikage where he
shaped the black flames and dubbed it "Enton: Kagutsuchi". The clearest and most indisputable evidence of these two being his Mangekyou jutsu are when he
uses both in the battle against Kaguya.
Even after Sasuke took Itachi's eyes to awaken the Eternal Mangekyou Sharingan, he has never revealed the Tsukuyomi. Instead his existing abilities were empowered.
Once the third databook stated that you would need Amaterasu and Tsukuyomi to awaken the Susanoo, but this appears to be outdated information. If anything, I'd believe that Kishomoto had originally intended to give Sasuke the same jutsu as his brother (with different preferences, perhaps) but decided otherwise at crunch time. As far as we know, the only character with the Tsukuyomi is Uchiha Itachi.
