Voltage regulator overcharging

In your first check, with the wires to the voltage regulator disconnected, there's no flow. Without flow, there's no voltage drop.
With the regulator connected, recheck the 10.8 Volts and then measure the next accessible spot (the splice pictured?).
If that next location back is 12. something, then the problem is in the connector.
If the next location back is also 10.8 Volts, then keep working back along the wire to the next accessible location. Repeat until you find a huge drop or lots of smaller but measurable drops.