which is the same one the ICJ uses, is that it ignores Article 4 of the Convention.
Consider the case of a conflict between three states. States A & B are signatories to the GC, but state C is not. If, as Sigler maintains, the GC is applicable to any conflict involving two (or more) signatories, it would also be applicable on C, because A & B
are both signatories. But that directly contradicts Article 4, which states (leaving out the last paragraph, which is not relevant to the discussion):
Persons protected by the Convention are those who, at a given moment and in any manner whatsoever, find themselves, in case of a conflict or occupation, in the hands of a Party to the conflict or Occupying Power of which they are not nationals.
Nationals of a State which is not bound by the Convention are not protected by it. Nationals of a neutral State who find themselves in the territory of a belligerent State, and nationals of a co-belligerent State, shall not be regarded as protected persons while the State of which they are nationals has normal diplomatic representation in the State in whose hands they are.
The provisions of Part II are, however, wider in application, as defined in Article 13.
In addition, Article 13 states:
The provisions of Part II cover the whole of the populations of the countries in conflict, without any adverse distinction based, in particular, on race, nationality, religion or political opinion, and are intended to alleviate the sufferings caused by war.
IOW, there is a specific section to cover those not belonging to signatory states - therefore, that means there are populations to which the GC as a whole does not apply.
I also disagree with your statement that the framers intended the Conventions to be applied as widely as possible. One of the primary differences between domestic and international law is that the latter has no impartial enforcement mechanism. This is particularly important in the case of the laws of war. If my neighbor starts shooting at my house, I can call the police, who will presumably arrive and force him to desist. In the case of war, if state A breaks the laws of warfare, State B has little effective remedy available. The only equivalent body in international law is the UNSC. However, the UNSC is a political body, and therefore its enforcement of international law is subject to the interests (political, economic, and otherwise, including alliances with parties to the conflict) of its members, in particularly the permanent members. Even if the UNSC is inclined to act, it is likely not to do so in a timely manner, and its proclamations are often not enforced. Even if the ICC functioned as well as its most optimistic supporters envision, it still wouldn't be good enough; courts, by their nature, are suited to dealing punishment and reparations
after the fact, but they generally do not function fast enough to prevent further violations in an ongoing situation - their resolutions can literally take years (note the glacial pace of existing international tribunals). The international system is particularly ineffective in the case that one of the parties considers its choices to be win or die (whether because it fears for the annihilation of its population in the case of defeat, or because it's a despotic regime whose leaders now they'll face firing squads in the case of defeat, or any similar scenario) - the leaders may be willing to take their chances on gaming the system once hostilities are over.
Because of that, the rules of war are designed to be somewhat self-enforcing. By limiting the applicability of the GCs to signatory states, and by the law of reprisals, which allows certain violations of the laws of war in response to a violation, non-signatories parties to a conflict have an interest to become signatories to the Conventions, and signatories have an interest in following them. Otherwise, to return to the example above, state B (the signatory) could have its (non-signatory) ally C do its "dirty work" - i.e. acts violating the laws of war that B is constrained from doing by the Conventions - but state C would still enjoy the full protection of the Conventions, just like B! (note that Article 2 is identical in all four Conventions - so if GC4 applies, all apply).
As for this
From what I can see there doesn't seem to be all that much ambiguity to it. On the Israeli side of the Green Line, people tend to be citizens of Israel and their children born in Israel become Israeli citizens. On the other side of the Green Line, that's not the case. If I were to travel to Israel, the visa I get would allow me entry to Israel, but not the Occupied Territories (at least that's my understanding of how it works). And Israel itself has not claimed sovereignty over the West Bank (annexation of East Jerusalem being the exception) because while the Green Line is an armistice line, it is viewed internationally and within Israel as a border...
If children born to the east of the Green Line were to receive citizenship,
that situation would be unambiguous - it would be Israeli territory. AFAIK, you don't need a separate visa to enter the Territories. Israel hasn't annexed the Terrirtories for several reasons, but none of them have to do with the Line itself. And whether or not the Green Line is
viewed as a border has no relevance on its
legal status.