Seeing a picture of the cover of the book mentioned above by Jim Dixon,

I realized: I have that book!
Dug it out (literally, from a stack/pile of boxes (I've moved a bit)) and there, on page 72 of Roll Me Over, Oak Publications, edited by Harry Babad, was the tune and words of The Gruen Watch Song.
The book only lists one chorus ("curved to fit the wrist") for the four verses. Joe_F's post above seems to have a better set of words, with a fitted chorus for each verse.

Here's the music, first (X:1) as in the book, with some of the bells and whistles (chord symbols and words), and second (X:2) as the raw tune.
Program "abcm2ps" will make a printout of either. Program "abc2ps" gets confused by some of the extra stuff in X:1, but prints the raw tune just fine.
"abc2midi" seems to work about the same on either.

I've added some extra "abc comment symbols" = "%" to hide the html line-feeds, so that it can be cut-and-pasted directly to a text file from the screen, or from the show-page-source listing.
Anyhow, here it is:

X:1 %
T:The Gruen Watch Song %
M:C %
L:1/4 %
K:G % Em actually, same key signature: one sharp. %
% ------------------------------ %
"^Em"E3/2 E/ B B | "^Am"A3/2 A/ c c | "^Em"B3/2 B/ G G | "^B7"A3 A | %
w: Shir-ley was a bur-ley cu-tie, danc-ing in the line. She %
% %
"^Em"E E B3/2 B/ | "^Am"A A c c | "^Em"B B B G | "^B7"F3 F | "^Em"E F G E | %
w: smiled out at the front row and I knew that she was mine. I asked to take her %
% %
"^B7"F G A F | "^C"G A B G | "^Am"A3 z/ A/ | "^Em"E E B3/2 B/ | "^Am"A A c c | %
w: home and she was sweet as she could be. The next day was her birth-day and she %
% %
"^Em"B3/2 B/ "^B7"A F | "^Em"E2 !fermata!E !fermata!E || "^Chorus:""^G"G2 G3/2 B/ | d d d B | %
w: want-ed jew-el-ry. So I gave her a gor-geous Gru-en %
% %
"^C"G3/2 G/ c e | "^G"d c B2 | G3/2 G/ G B | d d d2 | %
w: and the move-ment drove her mad. Then she mur-mured as we kissed %
% %
"^Em"B3/2 B/ B B | "^B7"A G F F | "^Em"E3/2 E/ B B | "^B7"A3/2 A/ F F | "^Em"E4 |] %
w: "Gee, it's curved to fit the wrist." It was the best time-piece she ev-er had. %

%
# stripped version, tune only, can use "abc2ps", which doesn't understand some of # the features of abcm2ps. %

X:2 %
T:The Gruen Watch Song %
T:(tune only) %
M:C %
L:1/4 %
K:Em %
E3/2 E/ B B | A3/2 A/ c c | B3/2 B/ G G | A3 A | %
E E B3/2 B/ | A A c c | B B B G | F3 F | E F G E | %
F G A F | G A B G | A3 z/ A/ | E E B3/2 B/ | A A c c | %
B3/2 B/ A F | E2 E E || G2 G3/2 B/ | d d d B | %
G3/2 G/ c e | d c B2 | G3/2 G/ G B | d d d2 | %
B3/2 B/ B B | A G F F | E3/2 E/ B B | A3/2 A/ F F | E4 |] %

%

I actually had a Gruen watch way back when, worn usually above my elbow, set 3 hours 15 minutes ahead of local time. But that's another story. It's gettin' late.

=//= Bob