I haven't been using Lilyponds tablature functions for some time, but now I am back and using the tablature.ly has helped dramatically in clearing up the looks of a score.
So, heartedly thanks to all contributors.
I have a strange problem, though.
The whole score/tablature looks nice and clean (I am using \tabNumbersOnly)
Except when I want to add a text markup after a "R" rest (whole rest for the bar, regardless of its time sign.).
Thus, this sentence: R1._\markup \rounded-box {"Impr."}
produces the word "Impr." in both the score and tab.
If I do r1._\markup \rounded-box {"Impr."} (replace "R" with "r")
everything is normal, i.e. the text shows only once, as in the whole score. But then there are two rests showing, and I would love to have only a whole (time sign. is 3/2)