The key in the wording IMHO is that the Phase One Search does not assume the person wants to remain unfound...
So the basic steps would involve paging Finney, and checking the cameras for any folks lying unconscious on the floor. There would be no need yet to check the cameras for Finney-lookalike people standing upright and flat out refusing to answer the page.
Quick glimpses would then cover all the bases for Phase One: "thorough" would stand for simple Boolean, that is, is there something floating out there or not, is there something lying down there or not? No face recognition, no opening of doors, no tracking of biosigns (which quite clearly is something they never do routinely even though they demonstrably can, so it's a big deal when it's done in "Court Martial").
The writer really nicely preempts technobabble concerns here, with the wording eliminating any and all futuristic tracking methods because the heroes aren't at tracking mode yet.
Timo Saloniemi
I love that TOS does that, finding a way to tell the story without getting caught up in too much tech if it is not needed. That's probably part of why we are still discussing it after all these years
