tabstaff and finger notation

[Walt North]

Is there any way to get TabStaff to show the same type of finger 
notation as Staff?

Or do I need to do it with text as in the second measure below?
\version "2.25.22"

#(define RH rightHandFinger)


\layout {
  \context {
    \TabStaff
    \tabFullNotation
    \revert TextScript.stencil
  }
}

theNotes = \relative c {
  \clef "treble_8"
  <c-3\5\RH 1 >4
  <e-2\4\RH 2 >4
  <g-0\3\RH 3 >4
  <c-1\2\RH 4 >4
  c^"3"_"p"1
}

\score {
  <<
    \new Staff { \theNotes }
    \new TabStaff { \theNotes }
  >>
}