what classical song/composer was on the A-side of the demonstration
tape that was packaged with the Sony Walkman 2 back in the early 80's?
(The B-side was a dance song called "Jungle Strut"

The answer is halfway down this Japanese page:
http://www6.plala.or.jp/tk_homepage/disco/disco.html

It appears to say that the other tracks or artists are:

The Square + Time Cycle

Actually it is not THE SQUARE/Time cycle. It is actually a very common
classical piece that I hear every year or so but have been unable to
get the artist/title for.

Perhaps you could have a listen to "Time Cycle" (the CD is made by
Sony):
http://cdnow.com/cgi-bin/mserver/SID=97153331/pagename=/RP/CDN/CLASS/muzealbum.html/itemid=451113

This piece by Lukas Foss has been mentioned as one of the top pieces
of classical music of the last century:
http://www.avguide.com/film_music/music/top100classical.html

Thanks for the attempt. I did listen to the pieces of Time Cycle. It
is not the song. I know that on the latter models of the sony walkman
a different demo tape was included that also had jungle strut, perhaps
Time Cycle was on that tape.

Geee.. 
I've even listened to that tape in 1982 as my bro' had a Sony Walkman
2...
I didn't think to prime myself by embeding it in my memory so I could
answer a question 20 years later!

The Jungle Strut track was the more memorable funky beat.
From vague memory, the A side 'may' have been a modern (slightly
electro synthesised) rendition of a classical song called Toccata
regards lot-ga