alternative volta 2 when empty

[Walt North]

What would be the correct way to code the following case?

I have a repeated section.  The first alternative volta has a couple of measure before going back to the repeat.  The second volta should just carry on with the remainder of the piece.  I'd like to have an indication of the 2. volta just to show where to carry on forward., The coding I have only shows volta 1. but not the (empty) volta 2.  I don't want the entire remainder of the piece to be under volta 2.  I rather not split out just the first measure of the remainder of the piece just to put it under volta 2. 

Thanks, Walt North

Simple sample below.

\version "2.24.4"

\layout {
  \context {
    \ChordNames
        \override BarLine.bar-extent = #'(0 . 2)
        \consists "Bar_engraver"
  }
}

ch = \chordmode {
  c1 c
  \repeat volta 2 {
    d d d d
    \alternative {
      \volta 1 { e e }
      \volta 2 {}
    }
  }
  f f f f
}

\score { \new ChordNames {\ch} }

if this were to be unfolded it would be:  C C D D D D E E D D D D F F F F F F F ...and so on.

There should be a brief volta 2. indication over the first F.