More coffee is not enough coffee for this! :(
Measuring for R, you put your meter at each end and knowing the current, measure the voltage.
Starting at 13v no load, with 20 amps get 0.3 volts across the thing, so R = 0.3/20 = 0.015 That R stays the same no matter what the current, so the voltage across (sag) will rise with a current increase. That is with the 13v staying the same!
Percentage of sag from 13v is 0.3/13 = 2.3%
Now no load is 26v, current is half at 10 amps. Why is amps half what it was at 13v? V=IR So what happened to the R across the same thing (length of wire or a fuse holder, eg) What is the voltage sag across that same thing now?
It could be those horrible watts things again!!! VA is the same (26 x 10 and 13 x 20) but voltage sag is about V=IR not watts.
Is the assumption that the 26v or 13v no load is from a supply with the same watts and voltage is across the same piece of wire?
But the solar controller has the same amps rating at 24v as at 12v so it can handle twice the watts of array at 24 as at 12, so current stays the same. That is the dirty secret--same amps at twice the voltage!!!! (How can they do that?)
But wait--at 26 vs 13 they used thinner wire to take advantage of all that, by not doubling the watts. R is double not the same. Current is half though.
So what are we comparing for an apples to apples deal anyway?