I was faced with a somewhat similar problem recently, with a thread on an engraver spindle.
As well as using thread-gauges and magnifying-glass, I made some brass test-threads in bits of bar, to what seemed the measured size, and tried them – very cautiously.
If they start to stick within 2 or 3 turns, they are obviously wrong; don't try to force them further.
Note the threads must be scrupulously clean so you don't risk a bit of swarf jamming or tearing the threads, and I lubricated them with a little spot of WD-40 or white spirit.
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(It actually turned out to be a 30tpi Unified Special, of all things!)