I sing unaccompanied (no guitar) when:

- I don't know the chords well enough to accompany myself competently and for one reason or another I want to do the song. (E., g., in retirement homes, I get a lot of requests for "It Had To Be You," and "My Funny Valentine" and the chords are not obvious to me, so I do them a capella. I've gotten such a good response that way that I keep doing them sans guitar. Gives my fingers a rest.)

- The song seems to 'want' a very lyrical interpretation and the guitar does not seem to enhance it. (On or near St. Patrick's I do a really schmaltzy "A Little Bit Of Heaven Fell" and it just doesn't seem to be enhanced by back up guitar. And it gives my fingers a rest on a day of long hours of playing.)
   (And, David I., your rendition of "The Sick Note" is a perfect example of a song working better without accompaniment than with one! An instrument would, I think, distract from the story.)

_ I like to use my guitar as a rhythm instrument on some songs. I know that's not really "unaccompanied," but it does mean having no help staying on pitch. If I had a bodhran, I'd use it as the sole instrumental background for some songs, because the rhythm back up is more important than the tune back up. (I do "It's A Long Way To Tipperary" and "Raindrops Keep Fallin' On My Head" and "Tea For Two" with my guitar as a rhythm instrument only.)

As for talking over instrumentals and not over vocals, it's simple. You can hear and appreciate music without focusing on it with your left brain. But you won't process lyrics while you're chatting or otherwise distracted.

Genie