"Note that 12.25V measured in RESTING state is 1/2 discharged for a 12V battery. About 12.8V is fully charged"
SAY WHAT?! The normal resting voltage for a wet lead battery is six cells at 2.2VDC, total 12.6VDC. 12.8V is a "hot" battery with a surface charge on it, or a different internal chemistry.
12.5V is a 90% charged conventional battery, rated from 11.6V to 12.6V for the working range from "dead" to "full", typically and nominally. At least, that's what I keep getting repeatedly from a wide variety of makers and sources.