Given the majority of the power consumption of a blinker is leakage current across the voltage-limiting zener, I thought I would try reducing the number of cells to bring the maximum voltage down under the voltage limit for the supercaps, and leave out the zener.

The 5-cell arrays I build generate just under 3.1v in direct morning sun. The voltage quickly drops as the cells warm. That's 0.62v per cell. The supercaps are rated for 3.0V, anything above this will degrade them. I will put together a 4-cell array, remove the zener and run some tests.