Back to Mrs Lemon's original theory.....

I tend to remember a song better if I've written it out, however, I don't sing with my eyes closed, infact I find it positively disturbing to do so (in front of people that is.)

I think remembering lyrics and music is so wrapped up with a lot of stimulie that are not auditory that it makes it very difficult to nail any particular trait down.

The eyes closed thing is probably more to do with being nervous, as Bagpuss said, than learning songs and then recalling them.

TTFN M'Lady P.