Without a schematic or block diagram I'm shooting from the hip. Power is provided with the wires probably tied together at the control panel. Check the connections you can see to be sure there is good contact and a tight crimp. A poor or loose connection will cause a resistance that would drop the voltage as you measured. If you could, isolate the wires going to that awning. Be warned it's probably a rats nest and you should label wires accordingly as you identify them. You can then disconnect and wring them out with a multi-meter on the Ohm setting to check they aren't shorted or grounded. Check to see that the wiring going to the awning lights is correct. It needs to be wired in parallel to get full voltage to the lights. If they are series wired the voltage drop from passing through other circuits could give a voltage reading you are finding.
