My advise is this:

Stop at the checkpoint. If they ask you your citizenship, say "US". If they ask anything else, then ask "Am I being detained?". The video examples are pretty good at that point.

They know that they have no real legal grounds to stop you. That doesn't prevent them from stopping you, since the vast majority of people will comply with their demands. I've passed through these checkpoints maybe a dozen times, maybe more, and have never been asked for more than a verbal declaration.

However, if I ever am asked for more, I will ask if I'm being detained, and will refuse to allow a search of my auto without a search warrant. I doubt if it will come to that though.