What proves a Richmond County surveyor is employed rather than self-employed in the United States?

The engagement paperwork does. A letter from the American firm setting out that it directs and pays for the work, together with a contract naming his Canadian practice as the supplier rather than an American entity he controls, is what answers the question. Invoices raised by a newly registered American company would answer it the wrong way.

The structure has to be visible on the page, not merely intended

Because TN does not permit self-employment in the United States, the documents must show somebody other than Damien controlling the engagement. A support letter should give the firm's legal name and address, his own name and Canadian citizenship, the profession stated in the Appendix 2 wording, the specific survey work to be performed, the duration requested, the remuneration and the person he reports to. Alongside it should sit either an employment agreement or a services contract between the American firm and his existing Canadian practice, with the firm as the client.

He should carry his licence certificate, degree parchment and transcript, and a certified English translation of anything not already in English. What he should not carry is evidence of an American registration in his own name, an American office lease or a second American client acquired since the engagement began, because each of those describes a business he is running there.