Possibility as a function word
Janus Bahs Jacquet, one of our resident linguists, in a comment, made an interesting connection to generic complement markers in Japanese:
I have nothing really to back it up, but it seems likely to me that ‘say’ has been reinterpreted as a generic marker of certain types of complement clause in Jamaican.
It ‘feels’ similar to how the marker と to functions in Japanese: its primary use is to mark direct speech, but it’s also used for things that can sort of be loosely compared to direct speech, such as the objects of sense and impression verbs, loose comparisons (act like, be like, look like), etc.
Assuming that seh is the right word in the last example, I think that and the one in the question are actually the same usage.
I'm in no better position than Janus to corroborate this theory, but from the few examples I've examined today, it feels plausible.
