I was in a discussion today with a friend of mine about the strength of the Mangekyo Sharingan, and the question of "can the Eternal Mangekyo Sharingan affect people without direct eye contact?". We weren't certain, and lacked the materials to get an accurate result. Could someone help answer this question?
I'm assuming you're referring to genjutsu, since Amaterasu can burn a person even if they aren't making eye contact, and Susano'o can smash a person even if they aren't making eye contact.
The fight between Kabuto and Sasuke and Itachi in chapter 586 suggests that eye contact is needed to cast genjutsu, even if it's using an Eternal Mangekyou. During this fight, Sasuke had an Eternal Mangekyou, and Kabuto didn't seem terribly concerned.
Kabuto: "Since I shut off my vision, genjutsu won't work on me. I tell you again, you two have no chance of winning."
However, Izanami can be cast on a person even without direct eye contact. This is explained in chapter 587:
Sasuke: "So how? How can ocular jutsu work without eyesight?"
Itachi: "The Izanami is an ocular jutsu... that works with the physical senses of yourself and your opponents."
Izanami is very special though, so this probably isn't the norm. After all, Izanami is an incredibly powerful jutsu that blinds the Sharingan that is used to cast it. The general expectation seems to be that ocular jutsu requires eye contact, regardless of whether the Sharingan is regular, Mangekyou, or Eternal Mangekyou.
Though note also that Itachi can cast genjutsu from his finger. So even without Mangekyou, it doesn't need to be direct eye contact.
I am going by the assumption that you mean, techniques that required eye contact previously, but after obtaining the EMS (eternal mangekyou sharingan) no longer do.
In which case, the answer would be no. The EMS allows users to tap into more techniques at less chakra cost. And more importantly, without the side effect of turning blind. But does not, for example, allow the Amaterasu to burn people without making eye contact. All though It does not have to be direct eye contact.
I assume you referring to use Genjutsu with Sharingan, because of physical ninjutsu did not require eye contact with the enemy to use it, like Amaterasu, Kamui, or etc.
Of course, it can. Even without using Eternal Mangenkyou Sharingan or ordinary Mangenkyou Sharingan Itachi can still use his Genjutsu through his finger (https://naruto.fandom.com/wiki/Ephemeral). Danzo can also use the Genjutsu from the Shishui's Sharingan eye that he stole to manipulate people even though the Sharingan eye always under his headband.
Eternal Mangekyo simply means that the backlash caused to eyesight by use of Sharingan and Mangekyo Sharingan is not experienced by the user. It doesn't affect the technique to such a degree that if visual contact was required earlier, it won't be later on. However, a lot of techniques of mangekyo don't require eye contact. They will remain as it is, however as user won't feel the side effects, it gives a bit of a power boost to the technique