Since this Article will enter into the discussion, everybody might as well have access to it without having to search the Red Cross website.

The text of Article 2 is short, but has a much longer legislative history which is reflected in the Commentary.

1949 GC III - Treatment of Prisoners of War - Article 2

Art 2. In addition to the provisions which shall be implemented in peace time, the present Convention shall apply to all cases of declared war or of any other armed conflict which may arise between two or more of the High Contracting Parties, even if the state of war is not recognized by one of them.

The Convention shall also apply to all cases of partial or total occupation of the territory of a High Contracting Party, even if the said occupation meets with no armed resistance.

Although one of the Powers in conflict may not be a party to the present Convention, the Powers who are parties thereto shall remain bound by it in their mutual relations. They shall furthermore be bound by the Convention in relation to the said Power, if the latter accepts and applies the provisions thereof.
The Commentary is generally held to be pursuasive, but not binding on a court, when considering the text of the Convention

Convention (III) relative to the Treatment of Prisoners of War. Geneva, 12 August 1949.
Commentary
Part I : General provisions

[all snips in this and following parts are from pp.19-27 of the Commentary]

[p.19] ARTICLE 2. -- APPLICATION OF THE CONVENTION
GENERAL AND HISTORICAL

[pp.19-20]
...
.... Since 1907 experience has shown that many armed conflicts, displaying all the characteristics of a war, may arise without being preceded by any of the formalities laid down in the Hague Convention.

Furthermore, there have been many cases where Parties to a conflict have contested the legitimacy of the enemy Government and therefore refused to recognize the existence of a state of war. In the same way, the temporary disappearance of sovereign States as a result of annexation or capitulation has been put forward as a pretext for not observing one or other of the [p.20] humanitarian Conventions. It was necessary to find a remedy to this state of affairs and the change which had taken place in the whole conception of such Conventions pointed the same way. The Geneva Conventions are coming to be regarded less and less as contracts concluded on a basis of reciprocity in the national interests of the parties, and more and more as a solemn affirmation of principles respected for their own sake, a series of unconditional engagements on the part of each of the Contracting Parties ' vis-à-vis ' the others. ...
....
[pp.21-22]
...
But the draft text said nothing about the relations between a belligerent, or belligerents, bound by the Conventions on the one hand, and a belligerent, or belligerents, not bound by it on the other hand. The ' clausula si omnes ' (4) which was included in the 1906 Geneva Convention -- but which was never invoked during the First World War, although it might appropriately have been in the case of Montenegro -- was omitted in 1929. But although the Convention was binding upon the Contracting States in their relations as between each other, they were still under no obligation in regard to States which were not parties to that instrument. The ideal solution would obviously have been that all the Parties to a conflict should be obliged to apply the Convention in all circumstances, i.e. even if the adversary was not a party to it, and despite the fact that the Convention would be a ' res inter alios acta ' for the latter.

There could be no question of reverting to the ' clausula si omnes ', which had fortunately been abandoned in recent times, since it no longer corresponded to humanitarian needs. The 1929 Convention had already departed from it by stating in the second paragraph of Article 82 that "in time of war, if one of the belligerents is not a party to the Convention, its provisions shall, nevertheless, remain binding as between the belligerents who are parties thereto". Thus the provisions concerning prisoners of war were given the binding force of which they had been deprived by the solutions adopted at the Peace Conferences. The fact that one of the belligerents was not a party to the Convention could no longer nullify its applicability.
Although from the legal point of view there was no way to extend the scope of the Convention, it was necessary to find one on the humanitarian plane. The Committee accordingly suggested to the Governments represented at the Diplomatic Conference of 1949 that the following two sentences be added to Article 2 :

"In the event of an international conflict between one of the High Contracting Parties and a Power which is not bound by the present Convention, the Contracting Party shall apply the provisions thereof. This obligation shall stand unless, after a reasonable lapse of time, the Power not bound by the present Convention states its refusal to apply it, or in fact fails to apply it." (5)

[p.22] The Diplomatic Conference also considered two other proposals (6) -- one, from the Canadian Delegation, suggesting that the Convention should also be applicable to a Power not party to the Convention so long as that Power complied with its provisions, and another, from the Belgian Delegation, which read as follows: "The Powers which are a party to the Convention shall invite the Power which is not a party to it to accept the terms of the said Convention; as from the latter Power's acceptance of the Convention, all Powers concerned shall be bound by it."

The fact that there was no objection to this principle was a sure sign that the time was ripe for this step forward in international law. The discussion turned solely on the conditions to be fulfilled. The condition underlying both the Canadian proposal and the proposal of the International Committee of the Red Cross was resolutive, while the Belgian proposal was based on a suspensive condition. As agreement could not be reached on any of these proposals, they were discarded in favour of the compromise wording of the present text.

The Rapporteur of the Special Committee gives the following explanation of the motives which guided his Committee: "As a general rule, a Convention could lay obligations only on Contracting States. But, according to the spirit of the four Conventions, the Contracting States shall apply them, in so far as possible, as being the codification of rules which are generally recognized. The text adopted by the Special Committee, therefore, laid upon the Contracting State, in the instance envisaged, the obligation to recognize that the Convention be applied to the non-contracting adverse State, in so far as the latter accepted and applied the provisions thereof" (7).

(4) [(1) p.21] Clause providing that obligations are binding on a belligerent only of ' all ' the belligerents on the opposing side (principal adversary and allies of that adversary) are also bound by the same obligations;

(5) [(2) p.21] See ' Remarks and Proposals submitted by the International Committee of the Red Cross, ' p. 9;

(6) [(1) p.22] See ' Final Record of the Diplomatic Conference of Geneva of 1949, ' Vol. II-B, pp. 53-54 and 107-108;

(7) [(2) p.22] Ibid., Vol. II-B, p. 108 (First Report drawn up by the Special Committee of the Joint Committee);
Rather long, but the history of the "accept" and "apply" clause has special relevance here.