Is this zeroing in on traces of 60 cycle hum in the recording?
Or else, won't it adjust an out-of-tune song to be in concert pitch? (Mind you, that would be extremely useful if you're playing along with the track and don't want to adjust your instrument, or cannot do so.)
To get it to the correct speed, I would go through my record collection and find a tune with long, sustained notes. Find the same tune on Youtube and get a pitch reference for the note using a digital tuner. Then adjust the record player to match the pitch on that note, down to 1/10 of a Hz precision.
(In the first place, why would you have a record player without a built-in strobe light for adjusting the speed in 2024, when this was a common item even in lower income households in 1984.)