Does anyone know the amount of time between when the villagers talk and have conversations with each other. I love that feature and it's hardly even here anymore. Anyone know the secret to it?

From what I know, it's a random encounter that just happens when two villagers run into each other. I'm not too sure though, as it's pretty uncommon for me personally.

I usually see/hear them happening, but when I jump in, it's too late.

It's happens randomly and if/when you here and emotion going off you should run to it. That's what I do.