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Tuners can be finicky devices. I’ve been very lucky with my Fender tuner, it seems to give me a clear reading in a stable manner. I have another one that came with one of my guitars, sometimes I’ll hook them both on the neck to sort of calibrate. That one is not as stable in it’s reading, flickers the green (lock indicator) a lot more but when I’m nicely tuned they agree with each other.
I will usually tune with a pick rather than a bare finger, I think it’s more reliable in producing a steady vibration in the string. I would imagine that it’s best to pick near the 12th fret (middle of the string) for optimum energy transfer, although I don’t do this, it just occurred to me that strings might vibrate slightly irregular. Speaking of irregular energy transfer: have you ever seen video of the Tacoma Narrows Bridge collapsing?
https://www.youtube.com/shorts/NpsDLes2bWM