While not entirely satisfying, here's an excerpt from a site titled Taps History... "The call of Tattoo was used in order to assemble soldiers for the last roll call of the day. Tattoo may have originated during the
Thirty Years War (1618-1648) or during the wars of King William III during the 1690s. The word tattoo in this usage is derived from the Dutch tap (tap or faucet) and toe (to cut off). When it was time to cease drinking for the evening and return to the post, the provost or Officer of the Day, accompanied by a sergeant and drummer, would go through the town beating out the signal. As far as military regulations went, there was a
prescribed roll call to be taken "at Taptoe time" to ensure that all the troops had returned to their billets. It is possible that the word Tattoo became Taps. Tattoo was also called Tap-toe and as is true with slang terms in the military, it was shortened to Taps.
The other, and more likely, explanation is that the name Taps was borrowed from a drummer's beat. The beating of Tattoo by the drum corps would be followed by the Drummer of the Guard beating three distinct drum taps at four count intervals for the military evolution Extinguish Lights. During the American Civil War, Extinguish Lights was the bugle call used as the final call of the day and as the name implies, it was a signal to extinguish all fires
and lights. Following the call, three single drum strokes were beat at four-count intervals. This was known as the "Drum Taps" or in common usage of soldiers "The Taps" or "Taps." There are many references to the term "Taps" before the war and during the conflict, before the bugle call we are all familiar with came into existence. So the drum beat that followed Extinguish Lights came to be called "Taps" by the common soldiers and when the new bugle call was created in July 1862 to replace the more formal sounding Extinguis