So ... what I do is try to tune intervals. Play in unison and try to get any beat frequencies out. Ditto for octaves and P5. P4 and M3 get more complicated.
When playing the P5 against a tone, you may hear a combination tone. EG if you play G over a drone C, you may hear the C one and two octaves down from the drone C. Those notes are more sensitive to pitch variation than the pitch you are playing. If a note moves one cent in the upper octave, the combination tone moves multiple cents. (A 1 Hz change in a lower octave translates into more cents than a 1 Hz change in the upper octave). So hearing that combination tone and striving to tune the combination tone to the drone C can help you tune your intervals in just intonation.
Which combination tones you can hear is really sensitive to pitch and your placement in the room and what harmonic content is present in the two tones you are trying to tune. Not to mention what kind of hearing loss you have and the peculiarities of what your brain has and hasn't learned to recognize. I've found it helpful to experiment until I find combinations I can "hear into" well, then try to expand my perception into neighboring note pairs. So with voice, I got something going with E,F,and G over middle C. Then I moved up to E#,F#, and G# against C# one semitone up.
I've been making some progress with this after being frustrated for years every time I revisited the topic. Planning some blog posts on the subject. I've actually made more progress singing than with the saxophone, so that's what I'll post first.
PS (edit):
Sometimes with vocal intervals my tuner shows the combination tone rather than the drone or my voice. For example, I can play E drone and sing G above it, and my tuner indicates C. When my G is in tune with the E drone, that C is 14 cents sharp compared to equal temperament.
I find this fascinating. Something a math guy would appreciate?