AI interaction

I have a feeling that the AI will more often make requests/demands if I have a unit roaming around their borders or in their territory. Anyone else?

It doesn't.
How the AI acts in contacting you for any reason has been looked at in detail by the TackyMango. Link here.

Seems there is a cooldown after each contact the AI initiates, after which an RNG is rolled each turn to decide if the AI will contact you for that purpose. While some factors, that you can see from the posts linked in my linked post, do change the RNG odds units being nearby don't have any impact whatsoever.

Thanks for link, Ghpstage. It settles the matter.