How did the Old Testament prophets expect the Gentiles to be reached?

The Old Testament prophets expected the Gentiles to be reached through Israel. Once Israel became the obedient vehicle and kingdom of priests, Israel would evangelize the Gentiles. They understood God would one day save Gentiles, but never envisioned a salvation of Gentiles apart from or without Israel.

Les explains that the Old Testament understood God would one day save Gentiles, but it had no idea it would be without Israel. The whole idea in Isaiah and other prophecies was that once Israel became the obedient vehicle, that kingdom of priests, then Israel would evangelize the Gentiles. The mystery revealed to Paul was different: Israel's blindness in part would continue until the fullness of the Gentiles be brought in, and this secret had been held in the mind of God until Paul.

Romans 11:25

For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.

What did Isaiah and other Old Testament prophecies expect Israel to do for the Gentiles?

Isaiah and other Old Testament prophecies expected Israel to become the obedient vehicle, that kingdom of priests, and then to evangelize the Gentiles. They foresaw God saving Gentiles, but they had no idea it would be without Israel, for Israel was to be the channel.