I guess you don’t think our politicians care which of them are in charge? And I’m not so sure about ironclad, we’ve withheld aid in past decades.
I really question exactly how Israel has significant influence over Egypt. Much less Saudi Arabia, which isn’t even a neighbor and has significantly more wealth and influence than Israel does.
The Saudis barely participated in Yom Kippur, from some brief googling they deployed a single battalion that saw a little bit of fighting in the Golan Heights. I honestly wasn’t even aware they had participated militarily.
Their much bigger impact was the oil embargo against the US, which caused rather famous gas shortages here and one of the most severe recessions we’ve ever had, during the Nixon years. Perhaps seeing the rest of the coalition demolished was enough? Though there were clear reasons for the Israeli victory that aren’t that difficult to understand. It’s far more specific than just Israel strong or something like that. That oil embargo ended up proving the power of OPEC though, dramatically strengthening the Saudi’s position on the global stage, which persists to this day.
Regarding NG, the main pipeline through the area for exporting Egyptian NG actually takes some pains to go around Israel, rather than through it.
https://en.m.wikipedia.org/wiki/Arab_Gas_Pipeline