Would the men of Pershing's Expeditionary force be considered "under the jurisdiction of the Republic of Mexico" as a result of physically being on Mexican soil? Absolutely. As a sovereign nation Mexico would certainly have asserted its right to arrest any of Pershing's men and subject them to the full authority of Mexico's justice system.
As I said before, the original context of the Jurisdiction Clause would entail FULL jurisdiction, as in:
"Greetings: You have been drafted and are now part of the Mexican Army".
As to law enforcement, while Mexico might have a de jure argument in regards to arresting members of Pershing's forces, the de facto reality would have been that any Mexican authorities attempting such arrest in 1917 would have been met with armed force.
Under international law, if you visit Israel with your family, can your 18 year old American citizen, non-Israeli citizen son be drafted into the IDF because he is physically on Israeli soil?
Again, you confuse being under the jurisdiction of a state with citzenship in a state.
No, I am applying the original intent of the meaning of the Jurisdiction Clause.
The Jurisdiction Clause was meant to imply FULL jurisdiction and, for that, you do not need to be a citizen. In 1972, while a legal resident alien with a Green Card and not yet a U.S. citizen, I had a draft number and a draft card and was legally liable to be drafted into the U.S. Armed Forces. After I became a citizen, that remained the case until the day I joined the Navy.
Legal resident aliens and U.S. citizens can be legally drafted into the U.S. Armed forces because they are under the FULL jurisdiction of the United States of America but a Mexican illegal aliens cannot be drafted because they are under the full jurisdiction of the Republic of Mexico. The former meet the original intent of the Jurisdiction Clause. The latter do not.
Mere law enforcement does not meet that original intent of the Jurisdiction Clause as every POW in U.S. custody was subject to U.S. military law but were never meant to fulfill the Jurisdiction Clause.
If the perversion of the original intent of the Jurisdiction Clause were applied in a fanciful "what if" scenario, a foreign power could capture one of the Aleutian Islands, as the Japanese did with the American Aleutian island of Attu, militarily hold it for 25 years and use it as a Birthing Center to fly in tens of thousands of pregnant women to produce tens of thousands of "U.S. citizens" who would then be trained by that foreign power and then, when they are young adults, be sent back "home" to the good ole U.S. of A. because they are, after all, "Born in the U.S.A."
The original intent of the Jurisdiction Clause of the 14th Amendment is crystal clear by the fact that, until the 1924 Indian Citizenship Act, being a full-blooded member of the Seminole Nation in Florida was considered enough reason that you were NOT fulfilling the Jurisdiction Clause of the 14th Amendment to be considered a U.S. citizen by birth even if you were born and raised in Okeechobee, Florida, U.S.A.
Let me explain this to you in a systematic way:
(1) The 14A says that people are citizens if they are both:
(a) either born in the US or naturalized in the US
and
(b) under US jurisdiction.
Both circumstances must apply in order to be a citizen.
(2) Examining criterion (a) we should be able to agree that being born on US soil means exactly what it says.
(3) Furthermore regarding crierion (a) we should be able to agree that being naturalized means someone who is (i) a legal resident of the US and (ii) has fulfilled the requirements set by Congress for earning US citizenship.
(4) The main point of contention seems to be criterion (b) i.e., what "subject to the jurisdiction" of the US means.
You say that it means eligible for conscription.
Your claim is clearly wrong. If your claim were true, all women born and living in the USA would not be citizens since only one of the two necessary criteria for citizenship would apply to them.
It is obvious that "subject to the jurisdiction of the US" has a broader meaning than simply eligibility for conscription.
"Jurisdiction" means simply (a) the territorial extent of a court's authority (e.g. the New York State Court Of Appeals has jurisdiction in New York State, but no jurisdiction in Nebraska) and (b) the range of matters which the court has competency to try (e.g. the Knox County Criminal Court has jurisdiction over criminal matters, but it is not a probate court and cannot rule in matters of trusts and estates in Knox County).
The jurisdiction of the US is clear: the Constitution gives the US judiciary full jurisdiction over US territory and full jurisdiction in all matters of law and equity.
Is any territory excepted from this jurisdiction? In certain areas, tribal land located on Native American reservations has been excepted from this jurisdiction. Another exception is the treatment of ambassadorial/consular premises of foreign nations as legally belonging to the nation whose accredited ministers are residing/working on those premises. There are no other exceptions.
Are any persons (not citizens, but persons) excepted from this jurisdiction? Historically, Native Americans resident on tribal land have been excepted from this jurisdiction. Anotehr exception has been consular staff and their immediate families. There are no other exceptions.
Are any criminal or civil matters excepted from this jurisdiction? No. Every single legal matter in the US can be appealed to the federal judiciary and can be enforced if necessary by the federal executive upon that appeal.
Persons present on US soil, whether they are on US soil legally or illegally, are under US jurisdiction.
Their children born on US soil are also under US jurisdiction and are therefore citizens.
Your point about Pershing's men, that obviously the Mexican government lacked the wherewithal to arrest them, does not take away the fact that they were under Mexican jurisdiction as far as the Mexican government was concerned.
Your other limit case regarding a theoretical breeding colony on Attu also doesn't apply because such individuals, while born on US soil and theoretically - not practically - subject to US jurisdiction at the time of their birth, by being "trained by a foreign power" in a foreign land could be shown to have substantively transferred their allegiance from the US to another power, thereby de facto renouncing their citizenship.
Likewise, if the US citizen child of illegal immigrants were to consciously choose to live in Mexico as a Mexican after attaining majority or if they served in the Mexican military or some other official government capacity, the same could be said of them.