According to the video posted, the song seems to loop at 15 seconds.
If you listen to the song carefully, it sounds like it's just a piano playing, and the tune is something similar to
C -> A -> B -> G -> A -> F -> G -> E, where it plays one note, then it skips a note and plays the next before going back up to the missed note, and the whole process is repeated.
Now, the song doesn't sound overly complex, so it may have been the reason why it is not included in the OST, regardless of how iconic it is or how many times it's played.
Another possible reason is that this tune has actually been used in some other work outside the anime beforehand. As a result, the production company may have been allowed to use only 15 seconds in the anime as background music, but is forbidden from putting it on soundtracks. My sketchy memory only recalls two other instances where this song is played: when Lelouch is around Nunnaly and when Kallen sees her mother on Refrain. I don't remember the song being any different in those cases, so its exclusion from the OST may have been a licensing issue (allow 15 seconds of the song to be used any number of times, but not allow the song to be reproduced in licensed soundtracks).