Any idea of when and how they found out David could really sing and could be trusted to rehearse and even become a huge hit?

Such a voice. Not a classically trained voice, but a nice pop voice.

https://www.youtube.com/watch?v=Z1Pgu6DHGHA

In an interview, he mentioned that he wanted to try it out.

He sang the theme song so apparently knew his talent early on.

I like the transition songs where can hear both David and the other singer each doing different sections.

Yeah but it's possible those songs without his lead were recorded prior to his recording the theme.

Shirley was aware of his talent. They used the other singer because the producers were obviously focused on selling records. But they had no idea of just how good a singer he actually was until his songs started selling.

David in this 1982 interview on Canadian TV, claims that he initially went in as purely an actor. They didn't know that he was also already a musician:
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