back when I got my first Teisco in 1971, I experimented on my own to adjust intonation. I would fret the octave note and compare with the overtone that you can achieve over the octave fret by slightly damping the string and picking it.
Then I would compare the tones by ear using the fretted octave note as a reference. Lengthening the string on the bridge the string would be longer hence the tone would be sharper.
The opposite would occur when the string is shortened on the intonation. The string length is shorter then the tone would be flatter.
I have my Squire Strat tuned in this manner. My Fender Strat is so used, loose, and worn, the intonation is always not perfect compared to my Squire where the neck is still fairly hard and stiff and not prone to wavering from perfect pitch.
Lengthening the string from 12th fret to bridge will lower the pitch - moving the saddle closer to the 12th fret will raise pitch. Of course you need to retune the open note and check the 12th fret again to witness the difference.