This sounds like utter Israeli nonsense/propaganda.
First of all why would Saudi Arabia even care whether Pakistan recognizes Israel or not? Did Saudi Arabia make a big fuss about direct ARAB NEIGHBORS such as Egypt and Jordan recognizing and signing a peace deal with Israel ages ago? Or force those countries to do it all while never having recognized Israel to this very day?
The most realistic and so far only official proposal to Israel is a Saudi Arabian invention and is called the Arab Peace Initiative which was accepted by all Arab countries without exception.
it is an interesting take from a Pakistani of all people. What you say is somewhat true.
I might add you ignore USA-Saudi alliance. Of course Saudis won't do anything to anger USA which is Israel's patron saint.