Exactly as the title says - crossStaff works for all stemmed notes, but 
quavers which are not beamed lose their flag.  I have resorted to 
merging in an extra note to get the flag, as in this example which shows 
the problem and my hack:

\version "2.23.3"
\score {
   \new PianoStaff <<
     \new Staff { \clef treble
                  \crossStaff {<e' c''>4 q8 r q q r q |
                               << q \new Voice { \voiceOne c''8 } >>}
     }
     \new Staff { \clef bass \stemUp
                  \crossStaff {<c g>4 q8 r \autoBeamOff q q r q |
                               q}
     }
   >>
   \layout {
     \context {
       \PianoStaff
         \consists #Span_stem_engraver
     }
   }
}

This problem does not seem to be affected by any other settings - 
especially (as shown in my example) not autoBeam[On]Off.  The problem is 
also present in the older versions of LilyPond at LilyBin.

Regards,
Paul

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