John believed Jesus was the Savior because Jesus had told and demonstrated to His Apostles and disciples that He was. John may not yet have fully understood scripture and the final fulfillment of the prophecy regarding Christ, but nevertheless, that didn't mean he didn't realize that Jesus was the Savior sent by the Father. I dunno, sorry, guess I'm still missing your point.
Jhn 20:9 For as yet they knew not the scripture, that he must rise again from the dead.
Why does john say "For"? For (gar) introduces a reason, How does John and Peter not knowing the scriptures tha Jesus must rise from the dead logically act as a reason why John believed Jesus was the Saviour? Do you not conceed that the context more logically implies John believed Mary, beause they dis not understand the scriotures,
So applying this principle to Acts, 13:48, that saying someone believed does not automatically mean that they believed the death and resurrection of Jesus, but could be referring to something else in the context that they were believing, what were the Gentiles told, that could have made those who had already been appointed to aeonous life by believing the gospel, rejoice and glorify the word, the pronouncement of God?
I would say, they, those who had already believed the gospel and by doing so had been appointed to aeonous life, rejoiced over hearing, that Paul had now been officially commissioned by God to take the gospel to the Gentiles, their families and friends and people groups.
[Act 13:47-49 KJV]
47 For so hath the Lord commanded us, [saying], I have set thee to be a light of the Gentiles, that thou shouldest be for salvation unto the ends of the earth.
48 And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as had been ordained [by faith] to eternal life believed [this].
49 And the word of the Lord was published throughout all the region. (The word of the Lord being here either the gospel itself, or the word of the Lord just rejoiced over: that the God of Moses was now yhtrough Paul calling Gentiles to become His people too.