What stops an international private airplane from landing outside of airports with a customs zone?
It is usually required to file a flight plan for international flights (with very few exceptions), and I'll assume this is the case for Canada/US as well, but I'm not 100% sure of this. In this case you have two options


You close your flight plan and let ATC or FSS know where you are, they'll note it's an international flight that landed somewhere without customs, and you're likely to end up in trouble.
You don't close your flight plan, and you'll trigger a search-and-rescue operation as you'll eventually be overdue, drawing attention to yourself, and you're equally likely to end up in trouble. Not to mention that you'll probably be liable for the cost of the search-and-rescue.


You could of course file a plan with a drastically reduced TAS, do a very quick stop, and arrive at the original destination within the grace period. I don't know if that will trigger any surveillance systems though.

If you don't file a flight plan and cross the border anyway, I'm guessing that you will indeed trigger some alerts though.