No regulatory requirement. There is no requirement to do anything just
because you are flying "near" the border, even if its an ADIZ. Those of
us in California fly "near" the ADIZ with Mexico on a regular bases.
When you are on downwind for Brown field you are less than a mile from
Tijuana airport (actually from the air they look like two runways for
the same airport). I have heard of pilot who flew their downwind a bit
too far out and crossed the border.

I'm actually going back down to Mexico the weekend after next. Crossing
into Mexico is very simple and easy. Almost as easy as crossing into
Canada.

-Robert