I forgot to ask where you connect your accessories, such as the speaker amplifier and any other higher amp component? Most manufacturers of such suggest the battery, but I would suggest the splice at the horn relay. Connecting any of these items via a switched or unswitched voltage source under the dash could be asking for trouble as the wires gm put in the harness are light gauge made to carry light loads. A high amp draw through smaller wires will cause heat build up. There is also more resistance in the thinner wires than a thicker wire you would run from under the hood. More resistance more heat, more heat more resistance and so on. Running accessories directly from the main spice with appropriate size wires and circuit protection in the way of fuses, breakers or fusible links is the way to go, imo.
The battery is fully charged at 12.8 volts. The reading you have at the battery of 14+ volts running and 12+ after you shut down is normal.
