Mystery solved! When the facts continue to not make sense, it is time to look outside of the box. I removed the backup battery and a/c power to the alarm system and the keypad "sounder" again went off at 6:00am. Turns out, when I placed a wireless weather stations (Weatherboy) on a shelf next to the keypad to monitor the temperature in the attic, the Weatherboy's alarm clock was accidently set.
Not only does the Weatherboy's alarm sound just like the keypad, it has the exact same cadence of multiple beeps that keep getting faster just like the exit sequence when setting the house alarm and it last for 1 minute. The Weatherboy is currently missing in action as it was last seen flying out the window.
Jim, January 2014