Just for fun (and because I’m procrastinating) here are a few other lesser used texts on the subject:
Berklee Contemporary Music Notation by Jonathan Feist (2017), pg 83 - “A tremolo a whole step or half step apart is notated as a trill, as shown previously. A tremolo greater than a second is notated with slashes between the two notes, which are each of the rhythmic value of the tremolo itself.”
The Norton Manual of Music Notation by George Heussenstamm (1987), pgs 54-55 - “The most frequently encountered ornamentation sign is the trill, which calls for the rapid alternation of the written note with its upper neighbor.” “There are two kinds of tremolo: the first consists of a rapid alternation between two notes a minor third or more apart.”
Hemidemisemiquavers … and Other Such Things: A Concise Guide to Music Notation by Dale Wood (1989), pg 45 - “A trill is always executed with the secondary note being the diatonic scale step above the written note. An accidental must be included if the secondary note is other than diatonic.”
Writing Down Music: A Practical Guide to Preparing Music Manuscript by Alan Boustead (1990 reprint), pg 38 - “Trills can be notated in many ways; by far the best is to include the auxiliary note in brackets. This will take care of trilling with any interval either above or below the main note.” [printed examples show parenthesized notes both minor 3rds above and below]
Preparing Music Manuscript by Anthony Donato (1963), pg 27 - “The trilling note is always the pitch of the note immediately above the main note as determined by the diatonic scale. Any chromatic deviation from this is indicated by placing an accidental next to or above the trill sign.”
If anyone wants to try translating Herbert Chlapik’s Die Praxis des Notengraphikers here are the pages where he addresses it. As I’m just reading it with Google Translate, I’m not entirely sure if it’s relevant or not.