The website cited by Catspaw and richardw early in this thread has Villanueva's story (Twenty-four Notes That Tap Deep Emotions) as well.
M. Webster's Collegiate suggests that taps may be an alteration of the earlier taptoo (note spelling).
Many years ago I attended a military school (cavalry-oriented). Tattoo and Taps were played on the trumpet every night by a young man who was a master. Every one listened silently as he played the 24 notes of Taps. There was always a space before the usual after-lights-out low chatter resumed. One of those memories that keep coming back.