I thought that the auxiliary note of a lower mordent (or other ornaments) was simply the note before in the scale unless the mordent had an accidental on top of it. However, I ran into this discussion providing a much more complex rule explaining essentially that the auxiliary note should be a half-tone down unless the note played immediately before or after the mordent was a full tone below or when the mordent is applied to a 3rd or 7th. Given that I never heard this before and that the full discussion leaves a lot of confusion as to how the accidental should be interpreted in that case, I am having doubts about that entire explanation.
Can someone explain simply what are the rules for playing the auxiliary note of lower (and upper) mordents, with and without accidentals? Examples welcomed.