South Sudan came into existence as a country in 2011 and has had internal conflicts and civil war since then. Aside from being outside of our guidelines here, I don't think we can say very clearly whether they will or won't sign it at some point. They have a lot of other things on their docket before this. There is no danger of them becoming a nuclear state in the near future.

India made it clear it would not sign the treaty because it divided the world into "nuclear haves" and "nuclear have-nots" — they thought this was inherently unfair, that some powers got to keep their nuclear weapons while nobody else was allowed to do anything.

Pakistan didn't sign because India didn't sign — they are bitter rivals.

Israel publicly didn't sign because it judged the NPT as infringing on its sovereignty as a state. Also because they had a secret nuclear weapons program.

Today these states are outliers but it should be kept in mind that many states were non-signatories until the 1990s. Non-nuclear states of note which did not sign for a very long time included Brazil and Argentina (who were nuclear aspirants). Nuclear states that were not signatories for a very long time include China and France.

You can see when various nations signed/ratified/acceded to the treaty here. It was not all at once.

As for why nobody brings up Israel — they do, sometimes. But the general way of talking about it is that Iran did sign the treaty (under the Shah regime), so it is bound by it unless it withdraws. The place where Israel gets problematic is that by being a non-signatory there should be sanctions attached, esp. since we do know that they do have nuclear weapons (which should make the Symington Amendment kick into action re: US arms exports). But the US's very obvious lack of acknowledgement of the Israeli nuclear program has been going on for so long that it is not really news, and everybody sorts of gets what it is about, and everybody sort of acknowledges the hypocrisy (and sometimes it is explicitly justified).