Pan size affecting evaporation time
The amount of energy required to evaporate the water stays the same, no matter what the size of the pan is, but a bigger pan could potentially collect more energy since the area in contact with the cooktop would be larger. There is also a larger portion of the water in contact with the pot, making it easier for more energy to transfer to it.

This question on the physics stackexchange basically ask the same question you do here, and states that the surface area of the water will have a significant effect on the rate of evaporation if the stove transfers enough energy. Given that there is no change in the temperature of the sauce during the reduction, the rate of evaporation will be proportional to the surface area of the sauce (as stated in the final formula there).