What would convince you that a closed source messaging app is secure?

Nothing. I barely trust open source after it's been in use for decades, reviewed by a myriad of pen-testers and battle hardened in the most hostile regions of the internet. I don't trust anything on a cell phone at all. That's just my take. Others may be more trusting.

Combo of reputation & provenance. Someone widely respected as a super-competent programmer and known to be somewhat of a self-directed loner. If Fabrice Bellard suddenly decided secure messaging was what he was committed to doing, I wouldn’t care if he did it closed-source.