12V circuit only works on shore power or generator

The RV battery is only 2 years old and I take good care of trickle charging. I took a meter to the panel to check the voltages. On battery power, the main wires to the 12v panel were 13.45 and the same was found at each fuse

What surprised me was that when I measured with shore power the voltages dropped to 12.8. I thought since the problem was happening on battery power, that the voltage would be lower on battery not higher.